{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Quantitative Finance\n",
    "\n",
    "Copyright (c) 2019 Python Charmers Pty Ltd, Australia, <https://pythoncharmers.com>. All rights reserved.\n",
    "\n",
    "<img src=\"img/python_charmers_logo.png\" width=\"300\" alt=\"Python Charmers Logo\">\n",
    "\n",
    "Published under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. See `LICENSE.md` for details.\n",
    "\n",
    "Sponsored by Tibra Global Services, <https://tibra.com>\n",
    "\n",
    "<img src=\"img/tibra_logo.png\" width=\"300\" alt=\"Tibra Logo\">\n",
    "\n",
    "\n",
    "## Module 1.2: Covariance and Correlation\n",
    "\n",
    "### 1.2.3 Lagged Correlation /  Cross correlation\n",
    "\n",
    "\n",
    "The correlation of two variables is an incredibly useful metric, however it has a severe limitation, particularly in many time series values.\n",
    "\n",
    "We would investigate the correlation if we expect a causation (note that we cannot prove causation) between $X$ and $Y$, that is, we expect that if we change $X$ then we cause a change in $Y$. An example of such a hypothesis would be \"if we spend more money on advertising, our sales will increase\". We can affect advertising spend, which we assume in turn will cause an increase in sales.\n",
    "\n",
    "However, the problem with determining this correlation is that advertising spend does not *immediately* affect sales. Instead, there is a period of time, a **lag**, between the spending and the sales increase. At the very least, people need time to get to the store!\n",
    "\n",
    "Computing this **lagged correlation** is a normal task, and a common one when analysing time series data. Another phrase for this term is **cross-correlation**, with a lag $k$.\n",
    "\n",
    "On terminology, if $X$ \"happens first\", we say it *leads* $Y$. If $Y$ \"happens first\", then $X$ *lags* $Y$. In many programming functions, the term used is simply \"lag\", and a negative lag value means a lead. Be careful with this though - some programs will only consider \"lead\", and positive values indicate this. Always check the documentation!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run setup.ipy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Investigating Cross Correlation\n",
    "\n",
    "Let's have a look at an example. One might suspect that interest rate is a leading indicator of inflation. If interest rates are lower, then they spend more, leading to the inflation. \n",
    "\n",
    "<div class=\"alert alert-danger\">\n",
    "    In this section we will manually compute the lag and then the correlation. In practice, do not do this and see the next section for methods that do this for you. \"Stand on the shoulders of giants\", and tend to use existing libraries rather than rewriting core components of your program from scratch.\n",
    "</div>\n",
    "\n",
    "Let's look at some data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "ename": "LimitExceededError",
     "evalue": "(Status 429) (Quandl Error QELx01) You have exceeded the anonymous user limit of 50 calls per day. To make more calls today, please register for a free Nasdaq Data Link account and then include your API key with your requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mLimitExceededError\u001b[0m                        Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[2], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mquandl\u001b[39;00m\n\u001b[1;32m----> 2\u001b[0m interest_rates \u001b[38;5;241m=\u001b[39m \u001b[43mquandl\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mRBA/F13_FOOIRATCR\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "File \u001b[1;32mc:\\Python311\\Lib\\site-packages\\quandl\\get.py:48\u001b[0m, in \u001b[0;36mget\u001b[1;34m(dataset, **kwargs)\u001b[0m\n\u001b[0;32m     46\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m dataset_args[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcolumn_index\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m     47\u001b[0m         kwargs\u001b[38;5;241m.\u001b[39mupdate({\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcolumn_index\u001b[39m\u001b[38;5;124m'\u001b[39m: dataset_args[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcolumn_index\u001b[39m\u001b[38;5;124m'\u001b[39m]})\n\u001b[1;32m---> 48\u001b[0m     data \u001b[38;5;241m=\u001b[39m \u001b[43mDataset\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdataset_args\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mcode\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdata\u001b[49m\u001b[43m(\u001b[49m\u001b[43mparams\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mhandle_column_not_found\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[0;32m     49\u001b[0m \u001b[38;5;66;03m# Array\u001b[39;00m\n\u001b[0;32m     50\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(dataset, \u001b[38;5;28mlist\u001b[39m):\n",
      "File \u001b[1;32mc:\\Python311\\Lib\\site-packages\\quandl\\model\\dataset.py:47\u001b[0m, in \u001b[0;36mDataset.data\u001b[1;34m(self, **options)\u001b[0m\n\u001b[0;32m     45\u001b[0m updated_options \u001b[38;5;241m=\u001b[39m Util\u001b[38;5;241m.\u001b[39mmerge_options(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mparams\u001b[39m\u001b[38;5;124m'\u001b[39m, params, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39moptions)\n\u001b[0;32m     46\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m---> 47\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mData\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mall\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mupdated_options\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     48\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m NotFoundError:\n\u001b[0;32m     49\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m handle_not_found_error:\n",
      "File \u001b[1;32mc:\\Python311\\Lib\\site-packages\\quandl\\operations\\list.py:15\u001b[0m, in \u001b[0;36mListOperation.all\u001b[1;34m(cls, **options)\u001b[0m\n\u001b[0;32m     13\u001b[0m     options[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mparams\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m {}\n\u001b[0;32m     14\u001b[0m path \u001b[38;5;241m=\u001b[39m Util\u001b[38;5;241m.\u001b[39mconstructed_path(\u001b[38;5;28mcls\u001b[39m\u001b[38;5;241m.\u001b[39mlist_path(), options[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mparams\u001b[39m\u001b[38;5;124m'\u001b[39m])\n\u001b[1;32m---> 15\u001b[0m r \u001b[38;5;241m=\u001b[39m \u001b[43mConnection\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrequest\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mget\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpath\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43moptions\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     16\u001b[0m response_data \u001b[38;5;241m=\u001b[39m r\u001b[38;5;241m.\u001b[39mjson()\n\u001b[0;32m     17\u001b[0m Util\u001b[38;5;241m.\u001b[39mconvert_to_dates(response_data)\n",
      "File \u001b[1;32mc:\\Python311\\Lib\\site-packages\\quandl\\connection.py:38\u001b[0m, in \u001b[0;36mConnection.request\u001b[1;34m(cls, http_verb, url, **options)\u001b[0m\n\u001b[0;32m     34\u001b[0m options[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mheaders\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m headers\n\u001b[0;32m     36\u001b[0m abs_url \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m/\u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m'\u001b[39m \u001b[38;5;241m%\u001b[39m (ApiConfig\u001b[38;5;241m.\u001b[39mapi_base, url)\n\u001b[1;32m---> 38\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mcls\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mexecute_request\u001b[49m\u001b[43m(\u001b[49m\u001b[43mhttp_verb\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mabs_url\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43moptions\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[1;32mc:\\Python311\\Lib\\site-packages\\quandl\\connection.py:50\u001b[0m, in \u001b[0;36mConnection.execute_request\u001b[1;34m(cls, http_verb, url, **options)\u001b[0m\n\u001b[0;32m     45\u001b[0m response \u001b[38;5;241m=\u001b[39m session\u001b[38;5;241m.\u001b[39mrequest(method\u001b[38;5;241m=\u001b[39mhttp_verb,\n\u001b[0;32m     46\u001b[0m                            url\u001b[38;5;241m=\u001b[39murl,\n\u001b[0;32m     47\u001b[0m                            verify\u001b[38;5;241m=\u001b[39mApiConfig\u001b[38;5;241m.\u001b[39mverify_ssl,\n\u001b[0;32m     48\u001b[0m                            \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39moptions)\n\u001b[0;32m     49\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m response\u001b[38;5;241m.\u001b[39mstatus_code \u001b[38;5;241m<\u001b[39m \u001b[38;5;241m200\u001b[39m \u001b[38;5;129;01mor\u001b[39;00m response\u001b[38;5;241m.\u001b[39mstatus_code \u001b[38;5;241m>\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;241m300\u001b[39m:\n\u001b[1;32m---> 50\u001b[0m     \u001b[38;5;28;43mcls\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mhandle_api_error\u001b[49m\u001b[43m(\u001b[49m\u001b[43mresponse\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     51\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m     52\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m response\n",
      "File \u001b[1;32mc:\\Python311\\Lib\\site-packages\\quandl\\connection.py:114\u001b[0m, in \u001b[0;36mConnection.handle_api_error\u001b[1;34m(cls, resp)\u001b[0m\n\u001b[0;32m    103\u001b[0m d_klass \u001b[38;5;241m=\u001b[39m {\n\u001b[0;32m    104\u001b[0m     \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mL\u001b[39m\u001b[38;5;124m'\u001b[39m: LimitExceededError,\n\u001b[0;32m    105\u001b[0m     \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mM\u001b[39m\u001b[38;5;124m'\u001b[39m: InternalServerError,\n\u001b[1;32m   (...)\u001b[0m\n\u001b[0;32m    110\u001b[0m     \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mX\u001b[39m\u001b[38;5;124m'\u001b[39m: ServiceUnavailableError\n\u001b[0;32m    111\u001b[0m }\n\u001b[0;32m    112\u001b[0m klass \u001b[38;5;241m=\u001b[39m d_klass\u001b[38;5;241m.\u001b[39mget(code_letter, QuandlError)\n\u001b[1;32m--> 114\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m klass(message, resp\u001b[38;5;241m.\u001b[39mstatus_code, resp\u001b[38;5;241m.\u001b[39mtext, resp\u001b[38;5;241m.\u001b[39mheaders, code)\n",
      "\u001b[1;31mLimitExceededError\u001b[0m: (Status 429) (Quandl Error QELx01) You have exceeded the anonymous user limit of 50 calls per day. To make more calls today, please register for a free Nasdaq Data Link account and then include your API key with your requests."
     ]
    }
   ],
   "source": [
    "import quandl\n",
    "interest_rates = quandl.get(\"RBA/F13_FOOIRATCR\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "interest_rates.columns = [\"Cash Rate\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c8b59fadc8>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "interest_rates.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "inflation = quandl.get(\"RBA/G01_GCPIAGSAQP\")\n",
    "inflation.columns = ['Inflation']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c8b5de7188>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "inflation.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "combined = inflation.join(interest_rates).dropna()  # Join by index, drop missing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c8b5e9e488>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "combined.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we comput the correlation, we need to normalise. To do this, we will change the values from absolute values to the difference from the previous record:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "combined = combined.pct_change()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f0c4d0f0358>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Hd3oU7z3PaoxpxXT2CmEXDI8/rD3MPc/uGu3TGDXSXtjVB7+zN3bZ3HA52uIEoM2ZeQKjWDEhD9wXkJPaStfl9WMJ8/BD5Y4+bCYDOWZDTCum0xX6LoWwC4ZCfUsPHb1eAlnaGjrthb3dqYhAqlYw1jf3AJkpMG6fP1QVE/x3Mu0Yd0TyVBdaoOT2YzPpyTEb6HL1HZDDhb1llD73P607zG/XHByV9xYMn6PNPchy9rasSHthVyPpWAKRDOpblYg9M4U90mNXfpa8XIWSPA3z2P0hK8Zm0pNjMcQckMOtmNEqeXx22yme3XpqVN5bMDzanR46g/dVqmbyY520F/ZEIvbh2Av1LUrEnok11R5/ZFUMJDdid/lCEbspLGLvCVoxuQlYMaMVsTd1uTNyMM8GVPsUoEMIe3oyUMR+tLmH6Xe/yJ6GPothByQQkDmmRuwZ6LGHL1AKRezJtGKUlafK8fURLQXsZiVijynswYfRatTT2uNO2vkkSiAg09Tlps3pQRYbs6YdajAGocAv20h7YVejqngR+7FWJ16/zM6THYM+dmOXW+spnonRW3jErlavJCrsj204xurt/VsVSsTed+Wp0+PHagwmT12+PuLZ6fIhSVBdaBuVz72914svIOP1y9qUXpA+1IuIPf2FXR2R4z2A6g49J9t7B31sdeQvzjFnprCHVcWoZY+JeuwPv13P396u7/c1EStPjbqIfuxqxO4LyH0Gky6XlxyzgeJc06A+d5fXz5ZjbQm/Ph6NXS7tvzPxex8su051RNhjY52jLT3a/SyEPU1RrZh4N15vcDHMibahCLsy8s+vzs9Ijz28KsZsHJzH7vH5aex0xf29LMu4vGF17HqlnNLnD2jJ09zgBhzRs63OXh8Oi5FC++AG1H9tPM4Hf/fWsL+rpq6Q/ZPtwu7xBfjAb9/ij2sPj/apJMyxFiczxuUCQtjTloGSp+oqx5NDEPajLT0YdBKzK/Lo8fhTtrp1tAhfoGTWD85j9/plTne64nrQ4b3YIWzg8AdwukPJU+jbVqDT5SXXYqDQZhxU8vRoi5OADC3D9OWFsIc40ebE7QtwuLln4BePEY62OJlWnotJrxPCno54fAFNFOIlT9VWAEOyYlqdVBVYKck1A8NfpLTvdBd/WX9kWMdIFj5/gIBMRNteGEzEHsDlDcS1wNQKmFDyVDm+yxvA6Q3VsUPfRmCdvV4cViVi73L5Ej6nhg7lO24bZsKsMULYRz55C/DWoWZe2nl6VN47HLXcdyiB0WDpcnm5/5X9wyq57XH7aO52U1Nkx2E1Rgi7y+vnl68eGLUA7USbk288sY3dpwZfyDFY0lrY23sVoTXqpbgRu2rFNHT0DnoVWn1LDzVFdgrtimUw3OjtH+/W873ndrPr1OATuckmfCNrUKyS8J8PhFqTHs+OcQUfzvDujqCItiyjrDy1KMIePSh3uoJWTI4JUOqSE+FUuyv4+uEJe1OXW5vJjFa55a9fO8gPVo/+7pLqAr2hBEaD5YUdDfzyvwfYMIz2IKp9WltkJ89qiKhjX3+wmftf3c97R1PTfiSRc1u1+cSIzCLSW9iDD3BVgY1ud9/qCgglT71+OSISGwhZlqlvcVJTZKPQrkTswxX2k0Hh+ce7x4Z1nGTgiRJ2NWJPNFryBv/+TGfsz1SNiqLr5NWyUbs5FLFHrw5UInYDRXZF2BMV11PtasQ+vO+pscvNuHwLVqN+yH79e0dbefPA0PsLne5wcbK9d9Sbz6k14U1d7pRHuluPtwNoJcZD4VirMhDVFNnIsxq14A9CFttwZ3RD5UwwCCpzmFP+Xmkt7KrQji+04Q/IMVu8hv/sZHviN0yb00uXy5fUiF2Nep7ecjLuBhMjhRpxh2+0AYlbMW6/KuxxInbVijFGWjFq9G016sm1xLZiulxeHBYjBTZF2BP53D2+AE3dyoPbMeyI3UVprplCu2nIEfsdq7bzveeG1oRKlpX8BcChxtH1tsNF9tQQonZ/QOain63hd2sODfjaLceCwt4ydGFXB6LqoLCHR8fN2v0xOrMwNQgqdVhS/l5pLeyqSFQXWoHYCdTeMGEfTGWMWupYU2jTBGa41Ran2nuZXemgx+Mf9eXqqgeuNQEzJp48lWVZGwBOxxV21YqJXADV1qM8aHazIeSxhw1ygYBMl9uHw2qkKCfxiP1Mpwt1wjbciL2py01JrpminMGVW6ocbe7hUFMPJ9t7h7TAqdPl0wKSg01dg/77ZHK0pYfi4PcwlMoyvU6i0+WLWDQUix63j/1nlGutH4aw17c4KbSbcFiM5NtMEcI+FiL2nLD7PpWktbCrX1BNoR2InUB1ev3a1GcwPqHm1RXbyLeZkKThRezdbh8dvV5WzhnH9PJcHn23flRXNXr8inCE76AEiUXsvrBcRVyP3RvlsQf/rYquNdgrBiKFvdvjQ5bBYTFQaE98QA2PJtuH6WE2drkpyTFTYIsv7F5/AK8/9mf1372NgDJbHIrff7oj9JkeONM96L9PFv6AzInWXpZOKgaG7rOPy7NwqiN+aSzA9hMdBGSwmfTDsmKUvJgNQInYwz5/dUY3WqtRG7tclI6ADQNpL+yqFaNE7LEqNHo9PorsZgpsxkFG7E4kSfHv9TqJfKtxUG0F/AE5YqBpCD4UlflWblpSw65TnWw/MXpJVC15qo/0wBPx2MPFP67HHlXuqL6P+p3ZTQbMBj0mgy5ipqUmuxwWI/lWI5KUWMTeEBQOo15KONka87y9frpcPkodFors8YX9S//YzOce2RTzd6/tPaP991DEUJ0FSRIcaBw9YW/o6MXjD7B4QiF6nTTkyphyh4XTHf3/reqvXzKzjGOtziEHPfUtTmoKFWF3WI10uX1a0YQasQ/n/hgOZzrdlOWm3oaBNBf2dqcXi1GnlSPGjNiDi2EqC6yDujHrW3oY57BoEWeB3aTZCIlw/v+9zg9X79H+/2SYsF9bV4HNpOeJjccTPl6yUYXdHGWVJBKxRwh7V+xIzK0lTyOtHnWWZTMpP1cagYU+V7Wzo8NqwKBXNuNIpOTwVFA4ppTmDisiUx/+khzFY48l7E1dbl7ZfYYtQTEKp9Pl5d3DrZw3WYlyh2JfqCI4uyKPQ8MUdlmWueTnb/D4e4NP2Kte96QSO+UOCyfahhZJj8uzaANvPLYca6O2yMbcqny63b4h2SVun59THb3UFCkz+DyrUWndGwwcmruV73K4M7qhcqbTNSKJU0hzYW/r8VBgM8VdwQhKVYzVpKcy3zo4K6bVqd0gQL/RWyzGF1rZ3xjyR9VSvIp8K7kWI4snFLKpfvjL34eKKs7qwiSDTkKSEvPYwy2IxrCIvdvtY1O9UkoWithjJ09VYc+xGCKSp+rg7Ah+p/HENZqGdhd5ViMV+dZheahq5VSJw0yB3YQzxsK0F3c2EJAVay46+lu3vxlfQOajS2uAoUXsqgieM7mIoy09w6rr9vgDHGjsHrD9QyzURGRNkV0JjIZqxeRb6XL54hYMyLLM1uPt1I3P16LtgTz5WBxv7UWWFfsUFGGH0OrTkMee3Ih916mOiDYUsZBlmcZON2UjkDiFdBd2p5d8m0mrroiXPLWZ9FTm2zjZlngy62RbL1UFVu3/+/NbYzGlNJeDZ7q19zvZ7kSvk7Qvdm5lHvvPdEUkd0eS6HJHSZIS3vdUFf/iHDONXS5tqvvQm0e4/vdvR5TGhZKnQY89LHkK9NlFSbXTHMGHMtEB9VR7L+PyLOTbjMOqegiP2OOVWz679RR6nQTAoaZIAfrvnjMU2IxcOL0Uq1E/JPviTKeL4hwzM8c5CMhwtHnonrPXr3w3u051cmSQq0frW3swGXSMc1ioGuSMN5xxeco9fzpO1N7Q4aKxy8386gKqg/74UHx2dX3IpJIcICTs7b0eej1+7T4bbtVUOC6vnxv/8A53P72z39e1O714/IERqYiBtBd2DwU2oxaxx+oXo3QSVKyYXq8/4WiuvddDQfDBhmDkOAjBmFqWQ5fbp/mlp9pdlDss6P2KcMytyicgM2qLlTQrJii4oPjgiUTsaqnk+EIrXr+sfS7bT7QTkGHzsTbNiomO2MOTp0BwF6W+Hrs6WCc6oJ7qcFGZb6XAZhxWxN4UjLxKHWYtedvaHXr/k+29bKxv4wPzKwE43BSySvwBmdf3NbJiWikGvY7KAuuQSgQbOlyU55mZXKoI1IHGoVfGeMO+z9XbBleJVd/sZHyBFZ1OoirfyulOV9yEcX+UB8WsIY7PrpY51o3PpzoYsQ+l5PHFHacpzTUzuyIPiIzY1VJHq1GfVCtm3YFmutw+1uxroqefEmbVshRWTAIowm7CbtKjk+J77FaTQYu+E4k63D4/Lm8AhyVUllRoN9HWk3h/7smlShMitarhZJuTH0q/hV/OA1cnc6uUm2/bKCVQoyN2UCpXVGF/fntD3AU26sM9vkB5CNVa9p0nlaXSm+vb4taxqyJtC/48N2oXpc4oKybRksOGjl7G5VvIt5no9Q7c1+elnQ28tLOhz8+butzoJCiym7Vyy/AB/bmgOH5hxWSMeimih8qWY220Ob1cOKMUYND2n8rpDhflDiuTSnKQJDg4DJ89XIifG6DNcjT1rU5qg3ZkVYGNgBw/6u6PcXnKsxfPZ996vA2TQceMcQ4sRj1lDrPWyiBRnB4fa/Y3ctmscnTB2VS+LSTsqsU2qdROu9OTtL1QX9zZgC5oYa7Z1xT3dWqRgbBiEqDd6aXAbkSSJHItxjhWjC9oxQSFPYFFSmoCTx3xQRF2XyDx/txTy5RoS63NXdqyihW9r0D3adjyd0odFsodFraf6JuAGwmiyx1BjdiVn3/vuV387o3Ye36qg4JajdTY6aa5263NTjYfawtZMVHllO1OLyaDDkPQ2+9jxQQ/ezViL7SbaHP2vymx0+Oj3ellXJ414mGOR7vTwzee2Mb/vrCnz+8au9wU2s3odVLYAqlQHuHZraeoG5/PhGI71YW2iIj97UMtSBIsm1ICMGRf+nSni3F5SuJ+fIFtWJUx6kA9J2j9Hdm/PaG/U1Ze92jWSGUwMDo+hARqWZ4SpcYbFLYeb2d2hUO7F6sLbYO2Yt7Y14TLG+B9s8u1n4VH7KrFNqU0l0CS9kL1+AK8uvsM19RVUmQ38WKMQEFFW3UqqmL6JxCQaQ9G7NA38gPl5lQbTqkReyJVCqooOMKEfbCLlIqCVRUHG7vxH1nPlzx/4UDBMqheCu/+Dvw+5lblsWMQEXtzt3tYy9TDCS1QCo/YFSumsUvxPOOVMsaK2HcFGxvNqnCw7UQHXW4fBp2kCXh4d0e7KWT/RO+i1OnyYjfptb8rtJvxB+R++4GHEtMW8q1qf5n4r//L+qP0ePwcb+3tU4ff1OWmNFhlVRRsJdEStGIONnazu6GTq+dVADCxJIfDYR775mNtTCnN0QSlMt9Ka49nUG0BeoO17+VBX3pKac6wKmPU7+qaugq+ZHiGCf9YBu/8fsC/a+724PT4tYhdC4yG4LObDXqKc0wxI/bDTd1sO97BwpoC7WfVhfZBWzEv7TpNgU0pSlCJEPagFTMlGHANpuTxrYPNHI8x0Lx9uIVOl48r5ozj0lllvL63Me5MUb3P0qqOXZKkyyVJ2idJ0kFJku5IxjFj0eH0ahspdLl8BGTI14Td2MeKcfsCyLLi5+ZZjdhN+oQiKM0OCI/YY0zLB2JKaQ7tpw7Avz7GcbmELQvvg6VfgvZjsPc55o3P53BzT8JNgX7x6n4++tC7SUn+RLcUACVi9/gCmkjHaxegRoEVwYf9TKdb26HqliU1eHwBNte3RQwaah07KA3AVHItxj5VMRGfe7Cdg5bA9Cn/3ni0VasqUr3bijzFY4f4lQ9dLi9/WX+E2mAkGl2Z1NTt1spnHVYDBp2kWUH/3aPUp6+cMw6AicV26luc+AMysiyz5Xg788eHBEoVw8H47OqsR/WlJ5cqg4dvCN42hJKnU6STfNXwFD1YkV+6A3Y/G3pR1xnwRw4+alWKGrGPy7cgSUNfpFSe17eWPRCQuePJHZiNOj69bKL28+pCG6c7XQn3pnH7/Ly2p5FLZ5ZrAQEoNqDJoLTube5yI0kwsVgV9sSeodf3NnLTn9/lh8/3bcjhHdoqAAAgAElEQVT20s4G7CY9500p5vLZ4+jx+FkXJ/Bq7HKTZzVq1mSqGbawS5KkB34DvA+YCXxYkqSZwz1uLH7w/G4+8df3CARk7cFVH+Rci6GPTaJWnFiNeiRJorLAOqiIPcKKsfVNpA3Ekvw27m35JrLfy2e9X6ekpBSmvQ8KJsDbv2FOpeKzJ7JtnyzLrNnXpCUnh0t/Hvuu4Pl0uXwxo031b+1mpVFXS3sbuv0v8such/nAlk/wN+OP+HTDPXxN/wSc2ASBADqdhFGveJ+28IjdbMDjD2gWkLrJhoragK2jtRme+BjcV4333T/z2b9t5IuPbsbnD2jCWZFvJS94P/R5cP1eWPtTnL+5gHmezfzshjrMBh0bo4S9sTMUsUuSpKxfCN5rG+uVWms1mp5YYsfjD3CizcmR5h7anV4W1ORrx6ocxCxRRbUrxuVZQJaZk9vFMvk9Th0/xIEzXTzy9tFBibzHF0BHgHlb7iZgtHOp6z56Surgyc/Aaz+EP1wAP5sKf7oQ2o5qf3e0uQeJgBaxmw16SnPNQ6rLByh3WPtE7P/YcIwNR1q5+4qZEd6zunI00br59QeVBOblc8r7/E5dfdrU7abQZqIkNzjzTiBAO9zUzVce24Isw9r9zREDjT8g8/KuM1w4owyLUc/SiUU4LIa4dsyZTpd2X40EyWhasBg4KMvyYQBJkh4DrgGS3nP0nElF/HvTCXY3dGoRp2qROCwGGtp6wN0FZiVx6Qx+EaqQVOYnVrLV2evFTi8OY8jXLbSb0BGgvasLKKPX48eoD1oNnafAG3XcniY+e/gr9Moenpn7Rw6sCygRnE4PS74AL36TBb1vUSs1cXT/ds4tqOn3nI639mBoP0wBdjbWt7Jieqn2u263T+k/EQiAuxOsIXHx+gOcbOulMMeEw6SD9nqQZSyd9dRKDVg6j0CP8vnU0IDbbWPnyZDwnul0M8HUGHF9xvZmJkqnKDvyFL/WPc7CXZsxyR5ckhWTaSGFhk4q/C1cIm+EP62CnDKYuIIbDIW86p+JzRw6v/BGYOYcvbbJhkqR3cRCaR8znrkNXI1QNhvji1/nh/6z+Hnv9bz9nh1nYzcTdA2U+U5icnuolRrwNR0AtRa6qwFevAPO7MCEg0dM98GW46wsP59Th3ZCi/LABQIy9u6jTDX4ofkgNO7mB/yNhbt3IndPZ+qRWqZNOB9alIZWM8zt1EoNNBzeRbvTS63UwDkmO6z5Jxz6LwvajvGm2Uve02awmkHSg8kO48+GCedDyXRleanfCw1b4eibTDuyhWdMTqa9nAe9p7myq4ErTeD76y941r+Ux3wrae+5hC9fPLXf+0XF4w/wUf3L5LdswXXV7+l5voi7bXdzv/+bsPYnMK4Oln0DNvwJ/nAB7efdjdS0j0t3P8Wl5h7sa6+FOR+EwgmclduGv6kDWpSol5xS7VnTcHWAJS/yZ+5uKvNMEe1yG1o7+dWLWzh3cjnXL6qKePn4QhtGfDQe3c1kfXHk4cO2W1TZsHEv+RaJcydFvhYUYfd0t2H1tTHP5qLYfSJ0f9RYwOKI+bl1Ol3c89fnmKTz8qnLJvCzl/exdesmlkwsAmD7sTZynfV8sCYHWg5hAm6c5OWt3VvxNNojZqgAutbDzLUalHsnt1y5D1KINNx+JZIkXQdcLsvyp4P/fwtwtizLX4r3N4sWLZI3btw46Pc63eFiyY/+y7dXzmBSsYVP/m0LT33hHOZXF/DtR9/gQ4duZ67hJFzza5h1LQcbu7j452v51Yfnc/W8Cu5+eifPbD3JtnsuRZKkuO+z7snfMW/b97E7CtFf9G2YcwOuHU9z6slvU21oQ3fuV1m5eRGXTTTzNflvsHNVzON4LMVc0XE7ZZPqePNgMzvuvVQpzXR3w/2zwDX4xKkfHZvNiznr+m/CxAs52Ozkfb9cy99umsnSzd+Aw2tg/s1w/jchr4p9p7u47BdreewiJ0sO/gLO9F9vC7BPmsjrLEL29vLxot1YO+J35mvVl/CatJinnHM576Kr+fxFM/nSPzazensDdcV+nr6kF/a/CEfWgrMFj6znsbxP89Gv/RgkiSc3n+DrT2zjjdsuoEY6w50Pv0RLQR0PfuJc8Djp+c8PsGz8HZ2WcRTc8ghyxXz++H/f4BOuRzAyiARYTjlvz7iLj69z8PpZG6jY+QeQB57q90h2dpvmMM/ahKl94A6FChJULiBQMp2nNh1nepmNWeU5yvs5W+H4BvDFCDAseRy3TudAs5vzpxRhsBfhKl/Ap17s4VLdRj5sWIMp0EubnINh/CJyz/00zLgq/mk07qHppfsoOPQsXZXnU/CZp/n5qwf41X8P8NoX5jDR7oWiSQD4mw/T+OcbGNd7ALds4I3APGSzg8v0m5RgIRbmPLjshzD/Fug+Ay/cBntWw7W/hbqPKK9p2AZ/vYoT1imsPP1Z3vn+B7C5Wzj52yspcNbjXfgZ8i7+BtiC3rgs07npCTqe/TbjdfGrTKJpMNUy7qbfQc05oR/KMr//+d18vPuPWOQYtqLZAdf+DmZcGfFjV0cj9b+5hmmeFPXDv2kVTLl4SH8qSdImWZYXDfi6kRJ2SZJuBW4FqK6uXlhfP/iVcGz5O++sfohaqYFS/xn2+KsovfxblExbQtOD1+JwN2Aum6aI19IvcbD4Qv7y5GpunSVTU1bEe6f9/Ht3N3d98FzyisrAXhIcPXOUm7fjJLz1K9j2TzYHJlNXmYOuYatyA7s72C9XESicwvS212mQCymQerDogaVfhNIZfU63tWQxC365C5Neh8WoY/u9l4V+eXoHNO7hr28dob7FyZ0rZ/CfXac51dbLJ86b0GfE/90bh2jrcXN+fgvTG56hWOqAoim8XHgj9+4o4emi31DqPAjTr4B9LyqRYNVi3HobWw8e42zdXsivgXO+DJY8nt12ijf2NfGzG+Zp7/HHdYfxtp1gseddFugO4Jd1tJeeRcmCa8AeiobeO9rK39+p51sfWckDe3P558aTAPz1E2exfFopf1l/hO89t5uZ4xy88NVlyh8FAtz8o7/yUdffuVS/Caa+D876FPt2bGDPlje5wnEEY48yjXXqcrDNuRqOvwOth3k7/yo+e+YaHvzMhXh8AT760AYevNyO3LCdF3Y0UJJrxmYy8PVLpiLLMrf9ezsXTC3m6nlKrTk6PUy6iIc2tfH91bvZ9t1Lyes5zM6Na/njusN85aIpTCrJ4VR7Lz9+aS8fP2cC86vzwVHBl9eb2NXg5HMXTOLXT77CE1caKQ9OqWVZ5q6ndlJXnU99cw+5FgOfv2QOVJ8DdiWyO+/Hr7GwpoBf3jg/9GX63HByE3ScCP5AgpJpUDaLe57bw1NbTkbcKztOdFCWZ6ZU78S57SlefvkFlrCdMn0X0td2ae+lEQjAi7fDe3/Er7fyF/dyFt7y/5g/bSKtPR7Oue+/XDm3gp9er3z3vR4/X3lsC2t3H+fO2R2UTD0br9HB9HG5TC8ywdF10NvG6u2neG1vIz+9fh46ZNj8N6hfD+OXQNMe8LqgaDI07YUbH4XiqfDnS0GnJ9DTwn7/OBzX/oRxa2/H1X6GffZF1PW8pTx/FXXKv7tOQcM29so17Kv5CNcsmkhLt5u/vHVUS2BeO7+SFdOUGevpzl4eeHErdzlewt57CubcAJULlVnrjn/DwVfYYqjjOekCJpTk8pHF4/n6E9t43+wyLu9+Bk5thnO+Ahd+Bwxm3I2HaH3wagq9Z9g/+3+YM02ZGT20/ghHm3u49+pZdPR6+eHq3SydVMR1C8eHPnZZ5u/v1LOpvi3iHAOyzG3/2saK6aVcNbcCapeBY1wfvUiERIU9GVbMSWB82P9XBX8WgSzLDwIPghKxD+mdOk5QY+xga2815dUXk1P/KiUvfwFelsjR5/JR71089pkvIr38HXj710zm1/yvEfyHLHDAy1myn7OMwLN/jDyuzgiBoCcr6Vhb+Wk+f2wFuz6zEvY8A9v/BTOu5OPPF3NuRRlW6X1c0fwQ28nn0i/+HqlwQszTLQQK7Qdo7fEwsSRq6lU+B8rn4G0/zF9e2MPa1+wcalKmtV2Nk7ntsmnaS11eP7944mVuOruGztoClj56Ma9c1kbtvj9x6YEfcLFZwus0w4cfg6mXKsnZN38BjXswOU+TRw9ra7/C+TcrNy/AlvpdvKw/AXNDArJlxyZeOH4aeB9/vG4C3/j3Tr48ZxGfWTox4tSPuI/zTGA7t1ctoqQh1O9mVnBhyIJqJYGorjpVPmMdJ0wTuLXr6/xk3Ltcf+j3sP9FpgF5ugI6i5dStPw2vvbCGT6av4P5e1eDrQg+9hxzKs6h6IE3+Z/HtlJdaKMk18zy886nvXcJX9zxGr4OWSlzm7sQCVi3ugijrZSr586NOG+vvwUAo0ER0orzJ/DMG68wTT+NL8ydzKEDTTwTKOamWUshWF2Rv3Unrc52Nta30mmtonTpJRCsk5aAveur2OWU2dnWwZcunAIzIi2SmPafwRwZWYahLE6KLImbU6VaGxZsSz9FXsFV3PLwU7xivh02/hkuuD304oAfnvkibPsnLP4s6ys+wQ8fO8wzwYi40G7ixrOqefTder5+yVSONPfwoxf3sOtUJ/dePZ+PnVPb96SmXAJAR289T+7cyW01FyqJ8zk3wOa/wsvfVe7nqx+A3DJ4+Gr418eV7w8ZPv4Ce/fuYvwrnyX32RvxW4u5wX03N1x2FXWTemH9LxV/vzM40F3zG76+phKr28y2+nwee+8Yel0pP7tpHj94fjcedx4r5i4E4I33jvGov5hP3XInE3f/Ft7+Dex4Ivg5W1lV9j/8omMZjd1ePlZVi75uBq89VUBBThWX3/B5eOlOJZh761fI9lL8zm4sAR3rz/kzF152jfYR5HlP8Ld/beO6onNZtekEzwQK+fr7V0B+aHW6DvjI7ABv/3MLn9h0mh+Mn80tS2po7XbzpC+HuRNmwtzYWpFskiHs7wFTJEmagCLoNwIfScJx+7L8DrYWfYzPP7qZpf4i3vNdxoGbA0h7V/OM5XreXevB6ddjX/kTmHE1Ow4f5/Ovenjgc1czv7qAM82tvP9nq7lrRSlXTjJBT7NSV+5sVSJSRwWUz+X5Nb3kNDWCTgez3q/8A+S9sY63D7dwoq2K9SU/5lBTD+/ox9E3ZRNicmkOG460RrQnCKeuWvGbu1w+/vLxs3hu+yl+/8YhrppXwbRyRejfOdyC2xfggmklzCjPxYuBVw3nc9EHr+Oe+3/F+/Xrec1xHQ9MvVQ5aH41XPlzQBGfD33vZa7Or+B8Qyh54/EFIhKnELkKdeGMyXiNx2L2W1c32TDqJW0lXbnDolWTzKxwYDHq+nihyvElNpVdz/Uf+jh0nmK3fzwr/7SLP569iItnlPLsUy9SOe065l88SYm0JYkc4Fc3zucDv1vP6U4Xt106FZNBR2muhctnl7N6e4NWoQPKwpRYyTGvdt5qKaWJiSV2NgcTqPtOK2sOSsKSXIV2E+1OL+8eaWVRTYG2+EVlYnEOqzYrgrSgOp9oKgusvH2opc/P43G600V5Xux7RWXF9FIem7mQNw8v4LwNDyoRp9GiVLY89VnY+W9Y8W244HacwWSeMWwG+OllE3jknXqufOBNWns8lDnM/OHmhVw6q787WakBB9hxskP5vHU6WPRJqLsJ9CZllghw07/hocuU3MbHV0PxZOwzxnH98/fwu8nvsnPSZ9jxUjv3TyqC0lx4f9/yy/E7N/KfXWfYdrydq+dV8D8XT6W6yMYLOxpYf6gFWZaRJIlN9W3k24xMGFcCFffCiu8os+/eNrDkseO/Z2g4Xo8vIFOSo3yv+XajUu5oMCvPyfSVcGITzScPsX7vcVxLv8GNl0VaJSuml6KT4J8bjrFq80k+uKBKq3oKx6DX8csb59P7yEa+/9wurpwzLmznpJGpYYckCLssyz5Jkr4E/AfQAw/Jsjy0rWMSYMnEIiQJ3j3SQoHNjDTzEph5NYF3jwE76HL5lD4kE5ZxvLuBE/JmrGYDSBKlxYV0msvZ4Krkysmz475HR++miMoMlSK7iT0NndhMer552XQ+9/dNHGzs7hNhhTO1TBH2ihg3AcCimgJ+f/NClkwsJN9mYt74fF7f28idT27n3587B51O4o39TZgNOs6eUIjFqKe60MZ7R1vx+AOsDcwjd/blvLr7DP6ArPUwiT7v6DLNWMKu2j+V+VYK7SbKHOaYJY+hBmJ6rSxvdmUoCWXU67h8VnmfvhhqLbvVpFe83aJJWIMrN7tcXpweP/6ArCRP9ZG35pyqPO65ahYPvXmEj5wdSjTfvKSG1dsbIh6yfJspZjmbJ1j6Zwj7jBbVFPDK7jO8eaCZ/3tpHwtrCrRGVIC2+rS+xcmNZ1X3OWb4TCy81FGlKt/KmeBSfKN+4CK00x0uppfnDvi6s2oL+c2e93Ge/L+w/XGY92FY9SnY8yxcfC+c97WIazYZQtdcVWDjprOrWbOvia9dMpXrF1YlVIY3vzqfHLOBNfuauCx8EDBEVXvYi+AzrymFDHmKHVbmsLBXrub5CRdz4HQ3Jbm9Wk+XWHzqvIlMK8vlQ4urI77bhTUFPL31FCfaehlfaGNTfRsLqwtCOTO9QfHrgzOUPGurtn9AcbAiJt9qimwrMPlimHwxu/c38T87NrBq1sI+51NoN7GoppB/bjiOToIvrJgU99xNBh23XzadlfvW8ey2U1qbhJHqEwNJqmOXZfkFWZanyrI8SZbl/03GMeNRYDdpzZHUVYYQqq4IX8ii7kJjMyq/kySJyaU5Ay7R7nR5I0odw98b4LqFVVpZ20B9PNQoJ56wS5LE5bPLtXr8QruJu6+cyeZj7dzx5HbWHWhizb4mlkws0h6+RTUFbKpv46Wdp5k3Pp/zpxTj9gXilocV2k19yjTdsSL2oPDOqlBEusxhiejeqOINq4FXo5CZFZGVEL+4cT53rYzMO6gDhz2sjr3cYdHEItb6gXBuXlLDf79xgdbDBeDsCYX85iML+OCCUGVFvtUYU9gVcZUiEucLawpoc3r55MPvMaHYzp8/tigiKg9/r0W1fYV7UlDYJ5XYtVLLcCoLrAkvxff6le39BorYQbG93g7MpKtgFrz1APzrY4qoX/b/NFGHsLJWfaRwf/+a2ay9fQW3LKlJuLbaqNdx7uQi1u5vimit8ds1B/uW7FocmqiDUlNeaDdxqsPF24daggFa/AKGxRMK+fql0/pExQtrFMHefKyNth4Ph5p6WFDT93tRCX+OS3KUezU/Tj8hr/ZZxZbFi2cqnvk1dZURnV9jMbPCwcxxDlZtPjGie52qpOXK03MmKckitdQRCOvwGPrCeoM12NawuunJpTkDLtHu6PXGFBe129/HzqmlJMdMntU44CAxtUwR9ljTtni8f34l1y+s4snNJ7nlzxs40tzD+VNLtN8vrC2gudvD9hMdvG92udaXJt65xGp96/EFIhYQQeiGnh2sry9zWGL2W1fFwqiXmFSSwwVTS1gZo4Y4GnXgsJlD34fVpOcjZ1fz/I4GdgV7zcSaLalEi4EkSVwxd1yEqBbYTBGbGKt4fX2jZlUoyhxmHvnUYm2AVVHXL5j0Om3dQTgTg1GnmleIpjJfidYSWdjT1OVGlkPdEPtjZoUDkHi7/CPQcgD2vQArf6ok8sPQ7CdDfBEdDBdMLeVke692r20/0c7/vbSPP647PODfljssvHWwmcYuN0snFg34+lhMK8/FbtKzqb6NLccVC21hosIetNjybaaYHUAH+qyunlfJkomFfPWiKQmd63ULq9h+okNbtFQygnXs6SnswU0M8iOEXe3wGCqB0yL2MGGfUppDU5e739Wb8SL2j51TywMfnh9sziQlNEgsnlDID66ZxSUzyxK4MgVJkvjJ9fPYds+l/PUTZ/Gty6dzQ1it76Ka0LLpy2eVh3UBjC/s0a1nPf5EInYzpztcfRqfeXwBdJLiJ1pNeh7+5GKml8euB444ftDDt0VFiJ84txadBL/4735AWfE5HNSILPq8fQG5j7BPKrHzw2tn88/PLIk5VVZXHM+pyosZ2dYW2akbn8/KubGrHCoH0XxOXcBTnsCUPc9qZHyhlWe9Z8HsD8K1v4fFn+nzuui8wnC5YJoSYLyxXylF/Ps7SnXbu4dbB2yQV5Fv0Xq8L500NGHX6yTmVysz1k31bRh0EvOq+uY2VMJn9ererfE6gHoG+KzK8yw8dutSaosTq0G/pq4Cg07ihZ0NFNpNETmsVJOWwn5WbSEGnaQtNwe0ToxdMYTdaoyM2KH/TYI7nN6Izo4qE4rtXBXsEwKJ9fHQ6yRuWVo7pKXEdrOB5dNK+fzySdrApb6vw2JgenkutcV28qxGSnPN/Ubsbc7IzpRun7/PlNMSvPHU6pYyhwW3L6A15lJJ1C+ORp0h2KI28x2XZ+WaukqtO2R/EXsi5NtMeHwBrcOkiifGeUuSxM1LaqgqsBELtV/MojhRocmg4+kvnquVtkVTkW/BYuy7wjUWql3TX84mnFnj8tjR4ITrHoK6D8d8TawVxsOhMt/KlNIc1uxrosPp5dltp8i3GTnd6RpwVap6XeUOi9bSYSgsqClgT0Mna/c3M6vCETEjj0YN0MKbuuVbjXS6vPijGsup7RfiWTGDpSjHzIrppcgyI7rqFNJU2HPMBn5y/dyI0qzQLkqhkdjl9WM26CI80ykD2BaBgEyX2xczYo9mcmkOLT2eYW1yPRR0Oon7PjiX7109K+Jc+ovY/QE5QqAVKybygbh2fiU/vHa29gCqEWy0HRPLn08ETdhjPIi3nh8qqcyNMagOhvw4/WK8vgAm/eAsiZJcM/dcNTN2GWACmA16rpxbwbNbT/bbrxuUfiwfWjQ+bj4mmlkVDupbnP02SNN6AiVJrAAumFrChiOtPPLOUVzeAPdepdyH7x5p7ffv1Pa950zq318fiIU1BQRkpTqnP38dQsJenGMKa+drQpZDvf9Vkj27AcWOgZGtiIE0FXaA98+v0iJLIOYuSup+p+FUFlgxG3Rxd3/vcvuQ5fgJvHC06H8UNhxeOWccZ4f5lOrsIdZ0WK3saAlrPxurKmZ8oY2bl4QqTlRLILoyxuPv688ngvp+4clTlalluVwYbJOQyGffHwVx+sV4/QGMQzjvT5w7IWGxjcWHF4+nx+PXernHY0F1AT++bm5CQQXArGAl0p5TcVaGAl6fcj8kU6yWTyvF4w/wq/8eZH51PlfPq6DAZuTdw/2Xdar305Ih2jAqdePztcrK/vx1CBf2UMSsDvzRG254w8p4k8WKaaWU5pqZkKB9kyzSVtijsZn06HVSRMSuCHukiOh1SsLvYFNsMe6M0bI3HsnY4SZZTC7NoTtsx6ZwQn3FQxFsb3A20x9qFj+6oiNWEjIR1BlCvKnzd66YwVcvmqIlqYdKnta6Nypi9/f12EeCBdUFTC3L4Z/vJXfzcjWw2dWfsPuVfEisMtihsqi2AKtRj8cf4JYlNeh0EmfVFrLhaP8R+5JJRSybUsxF02PbVomSZzUyNTjzHkjY1ec4PHGpteCOUQIMDGnwj4fJoOP5ryzj9sunDfziJJIxwi5JUp9t1nq9vpgiMrk0J27EHquzYzwq8qzYTPpRidijmdTP7EH1icOFPdYKx2hKg5sCqLvPqMRKvCaCuZ+IHZQKk69dMnVY03SAAnvsiCyWxz4SSJLEjWdVs+14e1K3QizNNVOcY+pX2If6XfWHxajn3MnFFNpNWgvjxRMKqW9x9lvWWZlv5ZFPnU1RzvD95uXTSphWlqvZO/2dq9mg0xYnAVoFVXQBRbI9dhW15cVIkjHCDn0324hlxYBiW5xs743ZklaL2BNI4OnU6H8MCPuUqK34wtF6yQeFvdPlpcvlG7AE02rS47AY+lgxXn9gSDd/rHLHVKButtHHY/cP3mNPFh9YUInJoOOxDcmL2iVJYmZFXr+DhWeIs6uB+NEH5vDvzy3VigLOnqDYKwNF7cni9sun8+yXz03otV+/ZCrXLwp1PVEj9uiS2FR47KNF+l9BGNGbbfQGN7KORrVQDjX23bV9MBG7eqyxIOzFOSalrj6GxaTWYqslj2rpXWWcNgfhlDksfT32IYqFukgm1mCbTPL789hH6aHNt5lYObucp7ecjLkbz1CZVeHgYGO31s8+mqEOwgNRkmvWavhBqavPMRsG9NmThV4nJVw++NkLJkXsrJQffLbbevreH8m2rUaLjBJ2R9RmG71ef0wrRt0eK1bJo1phEGsVYSwml+bQ0OGKuZH2SCJJElNKczgYI2K3mvRYjXotYteEPYGEYHmehdNRq0+HWhWjCrrdnNppqcWox2LU9fXYfaPjsat89oJJSBJc8at12m5Mw2V2RR6+gMz+07GDC28KrJhY6HUSi2oL2DBAZcxYwGE1Ikljx6pLBZlxFUGiN7SOZ8XUFNkx6KSYtoW232mCJXda9N/UN/ofaSaXxk8KF9pN2n6t6irIRCL20lxLn31BhyoW186v5Jc31g27Tj0RCmL0i/EMsSomWcwY5+D5ryxjfKGNTz28kf97aW+fWurBoi4mi2fHpMqKicXiCYUcaOympTv2XrljBb1OwmExxhz4UzG7GQ0y4yqCOCyGiNpUxYrpK9BGvY5FtQUR+yOqdPb60ElKrXwiTC3LZWKxHWcSdj0fLrMq86jMt8bMHRTlhFafnmzvxWTQUWwfOIlV5jDT2OUmECZAHt/QpvcluWauqasc+IVJIM/ad3Wh1x/AOMrT7PGFNlZ9/hxuPGs8R5p7GO7pVBfamFyagzfOAKFUAo3MNZ89oYjJpTkxK7PGGvm2vv2EPH7/iMxuRoKRTdWmGIfVGLExtNPji+vnPnbr0pg/V/vEJFqZMaHYzmu3LR/0uaaCW5bUcEtYHXo4hXYTLcFGYCfanFTmW/u0oI1FmcOCPyDT0uPRSiR9BigAABfsSURBVMY8/gD5Y/wBcARXF4Yzmh57OBajnvs+OBevPzDsCiCdTuLVr18Q9/dKVczILGVfWFPQ77mMJfJtphgL2EbXqksmmXEVQcrzLHS7fZrfHc+K6Y+O3th9YtKdQpspwmOP1x8+GrWWPTyBmg5TVrNBp9Ulq3j98qhaMdGMhIh4hrDaNhvIjwoCQV3Alhmf1di5y5OA2hWvocNFICDj9gUG3aOl0+UdEQ94pAnv8HiyvTfhbpNlMVafjrZXnQixhT0wYrbEWGGszFLGGgUxNmMRydMxiipWp9p76fX27eyYCBkbseeY6PX6aevx0NztSVjY1aXY4d0hh+qxjyQmg07rk6KSqtK/sYwQ9thEF1pAZt0fmXEVQcYFxaqhwxWzZW8iZKqwq8v0dwarJxKpiIHQ8v9eT6hOWvFtx3bka9LHsWIy5MFNFI9fzpiEYDIxxbPqMuT+yIyrCFKWa0YnBSN2tWXvIJfydvb6ht0PfCyirrbbfiIo7AlG7OrA6AwX9nSJ2KMf3BEs/RsrjGS5YzoRW9gzx6rLqG/coFc2OD7V7sLpVaZZg4nYZVmmM87uSemO2uFxx4nBRexqj/ZeT2TL37EeBcayYjwZlBxLFG8azK5GA7NBhy8g9ynjzZRBMDOuIoyKfAsNHb2hTTYGIexuXwCPP5ChyVPFK99xsgO9Tkpolx5QyumsRn1ExJ4Ovq1Jr48ZkY31mUayycZrTgQ1MAkf/Edqle5IkBlXEca4fCsNHS5cMXZPGojB9olJJ9RNmU+291LusMRcnBUPm0mPM5iMDgRkfIGx79tGT7X9AZmAnBkNngZDJkWhyUQd7Ny+cGEXHvuYpSLPwqn2XnqGkDzNZGF3WAwYgguSErVhVKwmvZaz0HbkSQdh9we0jUcyqXPfYBjq5iKZjtpCOrx5mvDYxzDj8qy4fQFOBfuhDEbYB7PJRrohSRIFwai9apC7AdlMeq1NQSq2WksF5qipdmij4sx4cBMlHRLdo4HaGTJ8Vifq2Mcw6hZmaivdwVTFZHLEDqGSx8FH7AbNY0/25sipQhUz9Xy9aXLeycYryh1jonnsviiPXQg7SJL0E0mS9kqStF2SpKckScpP1okNlYp8JSl4KNjl0DYIj13tLZJoZ8d0Q/XZEy11VLEZQ1aMN00i9ugHV90dx6Ab2+edbDwZZC8kk5jJU9ErRuMVYLYsy3OB/cCdwz+l4aFulaUK+2CqYtStsjI1Yi8YYsRuN+v7ROxj/QGIfnBTsVHxWMcfkPEHMkeskkn0jA5Ss43gaDGsq5Bl+WVZltUC53eAquGf0vAospswGXSc6XQjSQy4YXM4Hb3KpWSixw5hVswgI3aryaC1aEhbKyZNkr7JJBuvOVFMWvI0PGIXHnssPgm8mMTjDQmdTtKagdmM+kG1Re10ebGZ9Bnz5UZTVWDFYtRpeYhEsRn7Jk/H+mcUz4oZ6+edTNIl0T0amGN47Jm0gG1AM1mSpFeB8hi/+rYsy88EX/NtwAc82s9xbgVuBaiurh7SySbKuDwL9S3OQbcTuPGs8Zw7uShFZzX63LKklotnlA2646XV1NeKGcxMaDSIjsiysdzRmya22WiQ6cnTAZVPluWL+/u9JEkfB64ELpLVouHYx3kQeBBg0aJFw9sPbAAqgj77YBuATSnLZUpZbipOaUxgNekjNiBOFFuwjl2W5fSxYqKEPRvLHbNxlpIo0fdHpi1gG1b5hyRJlwO3AxfIspy8rdeHiWo1DFbYBbGxmfT4AjIefyBtxMIcr9xxjJ93MhEee3yiFyhl2oxuuFfxayAXeEWSpK2SJP0+Cec0bMYFSx4HazkIYqNaWr0ePx6/8iCMdbHoWxUTHJDG+HknE7cv+2YpiWLSRy5QyrQZ3bAidlmWJyfrRJLJUK0YQWzCW/d60iTy7Zs8zayILBHSZc3BaGA2Rg38aWIxJkpmXEUUwopJLhHCHox8x3or2Ghhz7SILBGEFROfvuWw6WExJkpmXEUUqhUz2KoYQWzUDpm9ERH72B40tQfXn14rZpNJuiwmGw0yfUaXGVcRhcNiJNdiIMc8tsUnXbAFB0inx5c2UWCmP7iJkC5rDkaDTK+aytiQ9hcfqqOmyDbap5ERqG0ZnF5/WBQ4th+APsLuy77kqTdNbLPRwKCTkKQYK5MzZBDMWGG/aEbZaJ9CxmAzxbBixrhAmoNWUZ+ITJc9IudNE9tsNJAkCXPY9onawJ8hwp4ZVyFIKXbNivGn1UYbEKsJ2Ng+72SiDWYiYo+JSa/rk1wf6/d1omTGVQhSitUU2tBas2LGePvbaCvGl4V17Nk4mA0Gk0EfmtFlWKI5M65CkFIiyx2V/t66MW5p6HUSep2U1eWO6bLmYLQwG3R9Vp5mSj5CfOOCAVHLHZ0ef1q1Ng2famvR6xifaSSTTLMXko3ZEOP+SJN7eyAy4yoEKUWnk7AYdfR6/Wm1GYEpPDnmD2DQjf2ZRjIR3R37x5TBwp6xVTGC5GIzGXB6fPj8ctpM7SMf3OzbSSi0mjJ7BrPBED7wezJs5akQdkFCWI2hnuzpcvNHVD34sm/vT2HF9I9Jr8Ptzczun0LYBQmh9mTX66Qxv8mGitmgwx1mxWSbwKVLBdNoYTLo+m7EIpKngmzCFtxFyeNLH4GM9lDTZaaRLLIxrzAYMjl5KiJ2QUJYgxG7Tkqfm1947OkzCI8G4fdHpnnsmXEVgpRjMxlwen3pVRUTtbIw6zz2NCpNHQ1MBn2flcmZ4rFnxlUIUo413IpJk5s/otwxC0XOk4WzlMGgJE+DC5TSpLldoohvXZAQNqM+uDWenDbL8oXHHsCUIUKVCqLXOUiSsmI5E8iuO10wZOxmQ/pF7Ppojz0zHtpEER57/5jDqmLU2Y0kZcY9Ir51QUKoyVOvP5A25Y7REVm2RezCY++f6KoYcwZ9VplzJYKUYjMqiaZejz9tIt9oKybbotdsHMwGgzrwy7KsDIIZdH9kzpUIUoraurfd6UkbgTRHLEDJvkSixy+nzXc1Gpj0OmRZuTe8GVY1Jb51QUKo+572ePxpI5CKxx5qy5pJD24ieHz+tMmHjAZmY2gzFk+GzW4y50oEKUXtyQ7p03sksslTZj24ieD1yxmzRD4VqIOexxfAm0bN7RIhKVciSdI3JEmSJUkqTsbxBGMPa7oKe7jHnkEPbiIIj71/TAblnvb4Ahm3zmHYVyJJ0njgUuDY8E9HMFaJiNjT5AEw6fUEZPD5A3h9Weixp1Fp6migBihun1LtlUmzm2R86/cDtwNyEo4lGKOkpbCHbWidaQ9uInj8mVXpkWzC98XNNKtuWFciSdI1wElZlrcl8NpbJUnaKEnSxqampuG8rWAUsBpD/eLSyYqBzHxwEyEb7afBYNYi9kDG2VYDdneUJOlVoDzGr74N3IViwwyILMsPAg8CLFq0SET3aUZ4xJ4uD0C4sGejyHl9mZUQTDaRMzpZ29s3ExhQ2GVZvjjWzyVJmgNMALYFl+FWAZslSVosy/LppJ6lYNRJx6oYdSWhO1j1kC4DUrLwZKH9NBjM+siB32HJnC7mQ74SWZZ3AKXq/0uSdBRYJMtycxLOSzDGSNeqGFCSY/6AjCHL6tgzrdIj2ZjCrJhMa7+QOVciSCnqAiVIv+Rpjzu99mpNFunUO380iLbqMinRnLS5hyzLtck6lmDsoe516k6nrfH0qrD7Iv4/W8jGvMJgMIfXsftl0QRMkJ2oPnu6RL7qANQdFPZsaing8wcIyOnzXY0GoeSpP+OqYjLnSgQpR7Vj0iZiV60YT1DY0+S8k4E3w/bwTAUR5bC+zEo0i29dkDBqAjVdpvehiD37PHa1R066DMKjgSmsairT1jlkzpUIUo5qxZjSJLLJZo9d7ZEjtsaLTyavc8icKxGkHHUBh0mfHgs5zIZIYc+kiGwgvH51c+bsuebBErnyNLPWOWTOlQhSTihiT4/bRq16yMbkqVdYMQOiRugur7LOQQi7ICtRk6fpIpCm6Ig9i0ROROwDo9NJGPVSaOBPE4sxEcS3LkgYa5pF7NELlDLJQx0IdUtAIez9Y9LrMjIHkzlXIkg56WbF9K1jT4/zTgZquWO6JLpHC7NRn5ErkzPnSgQpJ+3KHfXRydPsETnNY0+TRPdoYdLrMnLgz5wrEaQcmzG9FiipQt7jybyIbCA8mhWTPYPZUDAZdBk58GdOn0pByrl8djlunz9t+lZLkhT14GaRsKvJ0zQZhEcLkyEUsadLwJIImXMlgpQzrTyX2y+fTrD/flpg1mdmRDYQXm2BknjE+yPcismkzypzrkQgiEF4RJZNEXsoeZo91zwUzMbMnNFlzpUIBDEwBVsNq/+dLXj82ZdXGApKuWPws8qg+yNzrkQgiEG4mGeTyHl9anfH7LGfhoLJoAvlIzLos8qeO12QlYT7ppn04A6E6O6YGOawz0d47AJBmpCtEbtHJE8TIlPvj8y5EoEgBpn64A6E6BWTGGqjOMiszypzrkQgiIEasep1Enpd9lgxortjYoTPaDKp/YL41gUZjSps2eSvA3j+f3v3HmNHWcZx/Psr21agUiml3GFBKVIJIBRTIwgoIAIRohIIIhhMSEAJKGAgmPAHYChRowS8NFLEC3gDFQhyEwXCTS7SUgoCCmJNpTXIRRDabh//eN9tD4fd9uyeOTvnvPv7JJudnTMz5332nXnOO++8MycPd+wbRx9mo1HqGV05kZgNYfKaxD6+dvUVq9I3AvXSzWR1cGI360GDB+54u4i4cmD1uDtLGQ0ndrMeNJjQ+8ZZkls5sNr96y3wcMdhSDpN0pOSHpd0SRWFMqvKpHHcFTPeYh6Nt7TYC7p42tbTHSUdCBwJ7BERb0qaUU2xzKoxXrtiVgw4sbfirTewlfP/ajeSU4CLI+JNgIhY1n6RzKoz+EUTJR20rVg5EG/pZrChDf6PpLJGELVb8zOB/SQ9IOlOSfsMt6CkkyU9JOmh5cuXt/m2Zq1Z0xVT0Gl2K1a6K6YlgzcoTSxsBNF6u2Ik3Q5sOcRL5+X1pwFzgH2AX0jaKSKieeGImAfMA5g9e/bbXjfrhPHax37e4bvyxsqBuovR9UrtqltvYo+Ig4Z7TdIpwHU5kf9J0mpgOuAmuXWF8TqOfbtpG9VdhJ5Q6g1s7e7tvwEOBJA0E5gE/LvdQplVZbAlVlqLzKoxuF+U9sHf7neezgfmS1oErABOHKobxqwupbbIrBqldtW1ldgjYgVwfEVlMatcqQeuVWOwq660m7nKisasyZpT7cIOXKtGqWd03tutaKWOerBqlHpGV1Y0Zk1KbZFZNUodNVVWNGZNBhN7X2EHrlVj8M7k0s7oyorGrMlkD3e0dZg8scw7k723W9HcFWPrUuo49rKiMWtS6sUxq0apF9fLisasiRO7rcvah8SVtX+UFY1ZkzWPFCjswLVq9E0QE+QWu1lPcR+7rYskJvVNKG7/cGK3ojU+b9tsKJP7Nihu/2j3IWBmXW36lEmccdDOHDxri7qLYl3q7I/twm7bTK27GJVyYreiSeKMg2bWXQzrYsfP2aHuIlSurPMPMzNzYjczK40Tu5lZYZzYzcwK48RuZlYYJ3Yzs8I4sZuZFcaJ3cysMIqIsX9TaTnwd2B74PkWVpkKvNzi5utettWYOvX+nYq/V+qqEzF16v29/5W3/41k2dHU1Q4Rsfl6l46I2n6A5S0uN28E26x12VZj6uD7dyr+nqirTsTUJf9/73898P/vhrqKiNq7Yl5qcbkbRrDNupdtNaZOvX+n4u+VuupETJ16f+9/reuV/W8ky3aqrurpilnz5tJDETG7tgJ0QIkxQZlxOabeUWJcnYyp7hb7vJrfvxNKjAnKjMsx9Y4S4+pYTLW22M3MrHp1t9jNzKxilSZ2SfMlLZO0qGHeHpLuk/SYpBskbZLnT5R0VZ7/hKRzG9Y5XdIiSY9LOqPKMo7GCOOaJOnKPH+BpAOG2N71jduqQ1UxSTpG0sJcV3NrCGUNSdtJ+oOkxbk8p+f50yTdJunp/HvTPF+SLpX0TI5hr6btbSJpiaTL6oinoRyVxSVpbj62Fkk6podiem/eN9+UdNYQ29tA0p8l3TjWsTSUobKY2s6BIxlC08KQnA8DewGLGuY9COyfp08CLsjTxwE/y9MbAc8B/cBuwKI8rw+4HXhPleXscFxfAK7M0zOAh4EJDet9Eri6cVu9GhOwGWkc7ub5tauAj9YY01bAXnn6ncBTwCzgEuCcPP8cYG6ePgz4HSBgDvBA0/a+nevqsprrqpK4gMOB2/JxtXGu7016JKYZwD7ARcBZQ2zvy7mubuyhehoyJirIgZW22CPiLuDFptkzgbvy9G3ApwYXBzaW1AdsCKwAXgF2Je2Ir0fEKuBOUjKszQjjmgXckddbRhrSNBtA0hTSDnhhh4u8XhXFtBPwdEQsz8vd3rDOmIuIpRHxSJ5+FXgC2AY4kvShQ/59VJ4+EvhRJPcD75K0FYCkvYEtgFvHMIQhVRjXLOCuiFgVEa8BC4FDxzCUNUYaU0Qsi4gHgZXN25K0LelD6wdjUPRhVRhT2zlwLPrYHycFBnA0sF2e/hXwGrCU1Or7ekS8SPqk2k/SZpI2IrU+tqP7DBfXAuATkvok7Qjs3fDaBcA3gNfHsqAjMNKYngF2kdSfP6CPokvqSlI/8H7gAWCLiFiaX/oXKWFDOuj+0bDaEmAbSRNI9fS2U/66tRMXqR4PlbSRpOnAgXRBfbUY07p8C/gKsLoT5RuNNmNqOweORWI/CThV0sOk05MVef4HgAFga2BH4ExJO0XEE8BcUkvpZuDRvFy3GS6u+aQD6SHSDncvMCBpT+DdEfHrOgrbohHFFBH/AU4Bfg7cTepOq72u8pnRtcAZEfFK42uRznXXNxTsVOCmiFjSoSKOSrtxRcStwE2k+rsGuI+a66vdmCQdASyLiIc7V8qRqaCe2s6BHf8y64h4EjgEQNJM0ikTpD72myNiJbBM0j2k0/u/RcQVwBV5na+RkkpXGS6ufOr0pcHlJN1L6mvbH5gt6TnS/32GpD9GxAFjW/LhjSImIuIG8l1xkk6m/kQxkXRQ/TQirsuzX5C0VUQszV0Sy/L8f/LWltC2ed4HSS2mU4EpwCRJ/42Ic8YmirerKC4i4iJSny6SribXYx1GGNNwPkQ6mzwMeAewiaSfRMTxnSv58CqKiXZzYMdb7JJm5N8TgK8C38svPQ98JL+2Mekiz5NN62zP2ouNXWW4uPJp7sZ5+mBgVUQsjojvRsTWEdEP7As81U1JHUYeU9M6m5JaurX1c0oS6WB4IiK+2fDS9cCJefpE4LcN80/Io0jmAC/nftLPRMT2ua7OIvVX15nUK4krjxzZLG9zd2B3arqGMIqYhhQR50bEtrmujgXuqDGpVxJT3lZ7OXAkV1rX90M6vVtKuhiwBPg8cDqpVfAUcDFrb4qaAvyS1K+7GDi7YTt353kLqHGUxSjj6gf+QrpwcjvpaWzN2+un/lExlcSUt7M4/xxbc0z7kk5zF5JOXx8l9U9uBvweeDqXf1peXsDlwF+Bx4DZQ2zzc9Q/KqaSuEgt2sG6uh/Ys4di2jLvp6+QLt4voWlED3AA9Y6KqSwm2syBvvPUzKwwvvPUzKwwTuxmZoVxYjczK4wTu5lZYZzYzcwK48RuxZM0IOnR/KS8BZLOzGP117VOv6TjxqqMZlVyYrfx4H8RsWdEvA84GPg4cP561ukn3R1t1nM8jt2Klx8HMKXh751Ij6ydDuwA/Jj0GFuAL0bEvZLuJz1l71nSE/kuJd20dQAwGbg8Ir4/ZkGYjYATuxWvObHneS8BuwCvAqsj4g1JOwPXRMRspS8TOSsijsjLnwzMiIgLJU0G7gGOjohnxzQYsxZ0/CFgZl1uInBZfvrmAOmZ9EM5BNhd0qfz31OBnUkterOu4sRu407uihkgPWXvfOAFYA/SNac3hlsNOC0ibhmTQpq1wRdPbVyRtDnpqZWXReqHnAosjYjVwGeBDfKir5KeST/oFuCU/FhWJM0cfOKlWbdxi93Ggw0lPUrqdllFulg6+FjV7wDXSjqB9KUGr+X5C0lfkLIA+CHp+0/7gUfy41mXs/ar6My6ii+empkVxl0xZmaFcWI3MyuME7uZWWGc2M3MCuPEbmZWGCd2M7PCOLGbmRXGid3MrDD/Bw+MJE72lDlLAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "combined.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Directly, the correlation is not that strong:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10431055915017552"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combined.corr().loc[('Cash Rate', \"Inflation\")]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, if we add a \"lagged inflation\" value, we get a stronger correlation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "combined['Lagged Inflation'] = combined['Inflation'].shift(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Inflation</th>\n",
       "      <th>Cash Rate</th>\n",
       "      <th>Lagged Inflation</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-03-31</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-06-30</th>\n",
       "      <td>0.125000</td>\n",
       "      <td>-0.090909</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-09-30</th>\n",
       "      <td>-0.500000</td>\n",
       "      <td>-0.066667</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-31</th>\n",
       "      <td>1.666667</td>\n",
       "      <td>-0.142857</td>\n",
       "      <td>0.125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>-1.083333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Inflation  Cash Rate  Lagged Inflation\n",
       "Date                                              \n",
       "1990-03-31        NaN        NaN               NaN\n",
       "1990-06-30   0.125000  -0.090909               NaN\n",
       "1990-09-30  -0.500000  -0.066667               NaN\n",
       "1990-12-31   1.666667  -0.142857             0.125\n",
       "1991-03-31  -1.083333   0.000000            -0.500"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combined.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10431055915017552"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combined.corr().loc[('Cash Rate', \"Inflation\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.131542947831303"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combined.corr().loc[('Cash Rate', \"Lagged Inflation\")]  # Question - what does negative correlation mean?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f0c4904ce10>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rKDmBn0kpVwkh8oCVQoj3pZQb47BvTWfjtWI8A5Qgvh2oxuCjYBF7q2HF6M5TjSYWYo7YpZT7pZSrPM+PA5uA/rHuV5MkvFZMlrJjIL4dqMb+vR57sM5TLewaTSzE1WMXQpQB44HP4rlfTSfiNHWeJiJid7YTsXfksW+aCw8O9nWyajSaoMRN2IUQ3YHXgFullG1CLiHEDUKIFUKIFXol9S6MKyDdEeJsxZg8dnum/3zvHQn7oU3QWK2mHdBoNCGJi7ALITJQoj5HSvl6sG2klE9KKSdJKScVFxfH47CaRGC2YhLSeRokYpdStRTcnuybUMLeXKMe9VwyGk27xCMrRgBPA5uklH+M/ZQ0ScVp7jw10h3juIqSOWJ3ZKtRrm6nb9QphBb2Jo+w1x+O3/loNClIPCL204CrgZlCiNWev3PjsF9NMnCZ0h3tiY7YTftviUDYG7SwazTtEY+smCVSSiGlHCulrPD8zYvHycXEuldh/9rE7X/967B3VeL2nywMP91uTndMYMRu7N/oEM0pCp0V06StGE0MtDbCxw+lxeIuqTvy9O2fwWd/S9z+5/4Elj2WuP0nC7+5YjzpjomI2AP3bwxOyuurIvZg0xhoK0YTC9s+gA//F3YtS/aZJJzUFHaXE5qOqb9E0FCt9p2KkaN3gFJ2ggYoeSL2DHPE3uQbnJTXR/nurUFSGps8kXwqfu+axFO9XT02Hk3ueXQCqSnshqAnaqBL9Q71mIoCY54rJqEDlLL90ykNjz2vRD02Bfntkh2xH1gHcy5Pi6Z8SmIIe6ICvi5Eagp7Q7V6DCYO8eBoKgu72YoxRdTxwjulgClid5mEvbtH2AM7UKVMvsf+1ULY+i4c3Zmc42tiw7hvG7WwW5NGj7C3F7G73eovGoyav+FIfKe07QoYVow90+SBx7Hz1NkIwg72DF+LIFjEHijsrY2+PPdkZcXUHfQcPwUr9HRAR+wWx7jx2ovYn54FHz0Q3f4NK8bV4uv0SxWMhayFSEzE7mxW0Tr4798r7H3VY2ClbETrGTlQnyRhNYRdd95aD2cL1FSq59pjtygNYUTsR7bB3pXR7d+o+SH1bnJjIWvw5bGHO0Dp4AZ49572WzGtjT5BN3fOtnYQsRvC3nOI2tbohO1MvBF7iv3m6cCx3apTHrQVY1kMK8bV4vN0A2lthGN7otv/0R2Q21s9NyqRVMFYyBrAZgNbRvgR+5b58MlfoO5Q6G2cTaaIPaDzVNght0i9FijsRiXdc4h6jMQOqVwZn4rguBGxayuG4wfh8NZkn0X4GMGYPVNbMZbFLLZGpGfG5VSif2x35B55c52K3EpP8hwrxW5yZ7MvUgfPfC5hRuzGdu1N0uUXsZuFvQEycyErX70WKmLvNVQ9httSqqtSttuaF8Pbvt19aY/dy3v3wAvfTPZZhI/RcdpntI7YLUujSdiD2TFGs9/ZGPlNalwgpZPUY6o1y53Nvk5T8KxyFGbE7gpD2J2ehawhYEqBOo+w56nX2rNiIPzv/dgu1QQ/fiC87UOed7Mv0ku13zwaqjar7CCXM9lnEh7V2yEjF4pG6IjdsvhF7EGE3Tyf97Hdke27OlDYY4zeXK2w8Hddp3nvavZF1KCeh5vHHo6wt3oWsjb2Db4BShk5KlvG0S1I56nnZjSEPdzvy9thFqNlZkTrkLx+lYZq+OghcLuSc3wDKdV9IF1wfF/ij7fyn2oMQSxU71DXTrdCaAxoxa/+N+xfE9v+uxipK+y2DPW8OYgVYx7VWBOhz254dX3HqWPEKuyVK+CjB5U33RVwNvvSEEE9D3dAjrFde9FxsIjd1aI89sxc9X9WXuismJ4eKybc7712r3qMNRPC6DewZyYvYt/4X1j4v7Dvi+Qc36D+sC8bLNp+qnBpqoW3bo19epDq7dBzMGQXKk0wKkcp4e2fwud/j/1cuxCpKeyN1VA4UD0PFrGbhT3SC/PoDsjpBdkF6jHW6M2IKL/4V3zzxaPFaeo8hbarHLVH2BG7R9jtAbM7ZnZX/2flBbdi7FnQvY/qZA1XXI3vN9ZObqOyKhoZ/b4aqpVARTv2odYTHVd9Gd3n44U5KyzSFm+k7FsFyNgGhbldypLrOVhF7OALFFrqlB6kWApkagp7QzX0KFPPg3nsLTFG7IYdkNMrdsGo8dwY9VXw5dux7SseuFr8I3ZHZvgVjlfYO4jYg3ae1kNmjvo/qLDXqsrUZoOcnuFXqPHKXTasmD4nqmNHI86f/Q3euV2tBBUNhu1RtTm6z8cLo58JIr9/DN69B54+u+PtKld4jrkzuuOAarW5WtR9m+0RduN6MFpiWti7OFKqiN0Q9qARu2nu70gj9uqd0GOwep7TM3YrpqZSXWwFA2HFM7HtKx6YhRcii9gNK6a2g4jdSHcUQkXh3ojdbMUEidizC9TznKIorJhYPfZDgIDikZ4pEKIYmLZlvnqMVgyNiP3wlug+Hy+qt4OwQbeeKhKOBrdLjXvoCEPYayqjn6PH6BfrMRi69VDPjT4bQ9hTLG059YS9+bhakafHIM//7UTsef18EXM4OJvVTWlE7LlFsfutNZXKNpp4Lez4GA5vi21/sWIeoATqebgDlMLNimlTcbR4Ok8NYc8PIeyeVMjcCIQ9bhH7AdVCM+ayCdViCJUvX7sf9q9Wz6O1L2q7SMRevR3yS9V9EK3Hnt8PWo4HT0c2kBL2rvBcFzL6YxnWkdF5Cr6UR6MlpiP2Lo5xw+cUQWZe+x578cjIbrJjuwEZYMVEELFL2TaHtqYSCgbA+KvB5oCV/wh/f4nAFdh5mhW5x95wOLR902oaoAS+dEoj3RGUgAfrPPVG7GH2bThbVERmy1CfjyU1r+6QGhVrDKAKFuGtfw0eHBz83La+63sedcS+HxBwdFdyRt4aVO9QfnXhgOjLkt9PPda2k1VzbLeyKMvPU/+bLaBIqN6urun8fj4rJjBib6xOqXmfUk/YjSZ3Ts/gAgG+eUmKy9UNH+4skN6a37BieimhDlcw3v8lPDLa/wKqqYSCUjUPefl5sPqF6CcniwfOwHTHrAgGKJmayub0QL9tgkXsxgCl9jz2AGEPp6V0fB8goXe5bx/RcvwAdO+tAgYIfvyVz6qxEcEshi/nq5ZZj8HRRZ7Nx1U2R99xgIx91OeHv4XnL4nus0Y/U+FAdf1Gc73m91ePhlUWjMrl6nHMZeoxWp/96A5lzdrsbSP2eo+wu1qCrwFgUVJP2Bs8TapuPVWTPtjNbEQ7xSPVY7hRh+HVeSP2IkCGP+ChR5lqfhr2QFONqngKStX/I2ariulIEodqtxmgFEnE3up7bu5A3bFY7dftVi0Cv4g9S0Xrrua2WTHmCrC51ifsuUWq6dxRhVrjEY2SseoxFp+97pCyYXJ6qv8Do/LjB2HnYvU88PdrbYTti9TvG22Ua/RbDJ2hHmPNjDm4AbYtgCNfRfa5xmPqe+w5WLU0XS2hK/H2KDCEvZ2Ife9KVfEPma7GNlRHG7Hv8N2zbSJ207nH02evP5zUtNTUE/ZwInaj89QQ9nAjqJo9ahBNTi/fMSD8DI1iT+Ro3JTGcQsHqMd+49VjMvOUXUGmFAjbY2/2zaFj+OyHt8Gz58Oq5/wX2TDv3/A3zZ2nbqd/hRLYeQod+6JGBVoyJrztQyGlEoDuvU1WTMBvvvE/aoSrsLftJ9nxsYrkR8xWneTRROxGRkzZVM8xYhR24zdd/3pknztqCm4KPf1Y0VRU3UsA0b6wV65Q94QjUwVF0VgxzXWqdVM0XP2fke1/zZnnNYqnz/7uPfDM7MStCdEBqSfsRq3bXsTe0qD8bKMWD/fCbDyq9iuE+t8Q+HB99t4nqMcqT7qbITwFHmEvGqE6ipK5SHZgHrs9gikFnC2+TmtD2Pd5yrL7E99+zBG7PdP3m2WYrBjw2TGtTeqzxjwyRoXakR1T6/l++4z2bB9lRNZ4VM0Fn1eiWhX2rLaV+bpX1XH6jGobsX/5jvpc2emqEq87EHmGhyGAPcpUtBxrB6oh7BsiFHZzhokRkETTGezIVBWlcQ8E4mxRo0H7T1T/9xwcnRWz9T0VcIyY7Xstu9DUeXrId93FS9idzfDlPHXNbn0vPvuMkNQT9sZqQCgvLbsgdOdpRq6KLu1Z4V+Y5qgRTNFbx8IupeS2t/dwhAJaDhjC7qlQDCvGZod+FT4x7GykDDFAySMCR76CpX8K/XlXi5pP3ZbhE3ZjqPaez30WWGDEbnx/XivGI+DGb2e0usxWDHTcUqrZqypio6Ouoxv36E7lPQcO2Tea6917q0o9t8i/kji6Cyo/h9GXqMjQ7H9LCVveVRaKI8tXibfnLQfD2D6/n2r5VcWY8mjYZoc2RpZXb+5nKohB2EGVJVTEfnCdEmRj6o4eHmGPtINz05uQWwwDT/G91q2Hf+epEc3HmhJrsP0jdc0KmxotnARST9gbjihRt9nb7zzNzFGDXQpKI4jYj/k6X8AUsXdsxTy7bCevrqzkS1d/ju1cq16sqVQiaNgXoJqeB9b5+9WdhdsJyAArxhSxL39KdQCHinyNeWbySnweuyHsNXt8TelAj924oTIDI3bPb2e0ugx/tL0OTDM1lcrLNSL8jm7c9+6Fj3/vS0s0MMrSvY/n+D39j73+NfU4+hLoNVwJnTFddPV2ZaMMm6X+90a5EdoXtftVJZXRTbXsqr+K+BqRUrLzsMeGdDUri0rYIrNjqneo7yEzF7K6e3LZoxX2/qGFvdKzVoIxi2qPMhWQtTcldCCtjbDlPZWUYLP7Xu/midgNi82wSOMVsW/6rwpOKq5S/Rgtnd8pm4LCXq0uNvBYMbVta3ljwilQN1q4N1nTMf+IPUwr5vMd1fzv25uYdUIfavOGklu7DafT5RMem+ln6DdeCWm4UZSUsPHN+Cyw7PXAAz32ZnUcQ6RD5am7WlVFkFeitpES9q/1dV7u+Ni3T7/9e1oEZo8dfFaMV9gDIvaOWkq1e1W+dVaBErD2btxDm1R0B7D7M//3DDExcthzivxbC+tfg9LJyoYqGg5IX2S753P1OOBk9WhEuZH60rX7fC2P4nJVCZuH9ofB4wu3Mf3hRfxj6Q71neeXKntow+vhR8JHTR2REGPKYwhhd7th3SvqfSN7xshEi8Rn/2qh6k874UL/17ML1b1sWGxGX1skVt3RXapDPBCXEzbPU9bPmEuV1mxbEP5+40RchF0IMVsI8aUQYpsQ4s547DNsXK3qRjSa+Y3VvggtO1/9cIEecWujLzosiODCbKrxRY2gBDAzr90LYk91AzfPWcWAnjn88ZvjGFg+gVwa+WjFGl8Ou5n+E9RjuHbMrqXw8tWw5t/hbd8ehuUS6LGD+g6NGfZCCbsxgZgRsR/dqVL0xl+tWgHbP/Ls3yzspgwc8wAlCCrsLU63r+IOnOGx/rBKFzVEylxxZhe2f+Mu/oPPntsTKOwmKwb8B6Yd2wMH18Ooi9X/xnzxhs9e+bkqT5FHPPL7AyKKiH2vSdhHqMcIfPatB4/z5w+20T3Lwf1zN3K8oVHNpDn6EjiyDefeMGc3rN7uG3kNKuUxlkFKzTVtU1tXPK2+txn3+PqzjJHkkWTGbHpT/e6Dp/m/bszwWF+l/i8cpLJuwo3YG6rh2QtgzmVtz33XEqVBJ14Ig05X16oRMHQiMQu7EMIOPA6cA5wIXCmEODHW/YbN9o/gmbNU5xy0jdihrc/eUm+K2AeqGzfUSktmAq0YaHfekh2H67n8b5/gdLv529UTyc/OYORo1bRc8skSVaEECnsPzwx04Xagbn1fPe7+NLzt28OYntdvrhiPCFdt9lkjAXPBNLQ4WbDxIE1NjczdcIT39thoOLKHN+e/A4C7/yTVEtnrGR6eERCxG3QQsf9mwV7G/vpd5qzcj8zKb2vFfHA//Ocm2LVMZUM0HfNGfLJbD7bu2sNFjy/l4y1V/p878pWKuk/6rhKBPZ/5R7B1B9X1YpxXjsljNyqBQaepx17D1KPhs1cuVx2ARqvMaNGEEUxIKdl3rJEFGw/iMkfsRYawb1HX9ud/VxFkCFxuyR2vrSU3y878W6dSMaCQ6prjbKpq5ltLetMq7cx7/mH2VPssAyklbndAFN/SoCp1c8ReMDC6BWvAlMs6saWnAAAgAElEQVRuitqP7YYF98HQmVDxLd/rhQNRg7N2hrdvZ4vqwBx5rqrAzGQXKhE3V9g5PcMTdpcTXvmOmkrB1QJffej//sY31bUy9AywO6D8XNXHEo8WdQQ44rCPycA2KeV2ACHEi8BFwMY47LtjBk5RGS47PsY1eAaioRpbn1HqPaPp3lyrBgAZtDb4Ouq8TeNKKBrm3aSu2Umm3Uamw3NDupzQcpzWjDz8LpOcXjTXVrHvcD1IN6K1EZmZy5G6Zm6eswqnW/LC9VMY0UeJgr2PqvMyD29EZuznWGZvjh2uN++RkuKx2HavUPsMoKBbBj1zTcK77QP1uPtT3G7J8WYnBd0yVKvE5vC7qF1uSeXRBtwS7HUHQLpw5fX3vu+oOcoAaDtACTi8eQkeA4SjB3ZRXVXHmj3HeGf9AT7eUkWz083mrBZctkwOylxy3PUc2fgRrXY70/95gN/klzHT7al8HN3a7F99KcEj9p1791EGzN/WwPC+vbnnjfWcmZdHdvUBjni+I1vjEQaseREbULf0bxw76aeUAodsxWzffoSCGgeHW/axJ7OBa575nEsnlvL9aUNw2G0UffAgubZM9pR/l9xtcyla/yq7t3/JxsYCPtx8iFmb1jKOAt5eupNThvaihDx6NNey42A1vbZ8TPeMHHY5BsPheqrrnYzMLGb5smXcv3guC1o38JzjUp59aCE2myA308ET7l7k7N1GTVUdQgicLjfr9tbw2fZqNh+oRQJCCA7UNHKwtplMWtmSfZj5uwSle2sY1S8fUTBQtdI+fVwJUslYuP4D/xaQh+c+2cmq3cd49JsVlPbI4elrT6L1YRefH2jkeJ98vux9NrOq3mP2n9/h5nNPYuuhOt5eu5/6Fidnjyrh4vJcBnVrJKNmJyXAoYy+1B+upzgvi+6FA30L1uQWUdvUSn62v5DWNzvplmHHZhPe11pdblpzSsgB1RopHqkqh7k/ASlpOecR9h7x96YHdO9L04GtVAXcF8LVTGnPPBwZpuPu/FgFBCdeSE1jK9X1vpTdQplDj5bjNB7ZQzdQfQbdevgJu8st2VPdQGB11XPxfRTs+IiqmQ/Tc+lvaVjzFod7e/pPpJsBG9+ieeBMDtVKoJ5u/c+m5IvnObB6Po1lars++VnkZMZDekMTj733B8zhRyVwchz22y4ut8RuE6oDp/QknNsWccXWs3iupoqD9ZkMhnYi9gZfR5gxve+xXV5hf3PNPu55Yx352Rn85MwRXFzRjw9WfcnZwIOLDpDj3sJNXxvKscYWqmsycB3fyYUPL+J2x4t8w76YU5ofQ2KjqHsWL97gE3UAcnshc4qZ3rAegZsHltXz0uJFfqd3m6MH37cvZfbD79GM/41qEzCzvA9XnzKIqX1asR1cpyKfozu49el3mbfDzWWTBvDrgz8ks/9YuPAxABZvreK3b29i8wEllu9l/pyvZD9uav2Jd9/DRCULsuDBBdvJOryFplY3jtU7uQ1YunAe59jsNJHF3KWruPcjZav0LcjmyskDmVXem6wXnFw0sUzNmf6ff3JN0WaOu4dRUVLC29sGMNNznNfXHebrpRIhhF8lsrtOsLf6CBP6dyMLaG2o4aF5m7AtW8+dDnjiuzMYM7gfTy3Zzq4FefTa8jnnrFff0S321/lZRjMfuio4fctc/rChH49kwg/mHmK5/JTnu+Uytlczy34wk8c+3MpfP9rOqysr6UYTa7Ne5V+umfzqiQ2MEoK3s+Dhp5/jTfdp5GU7+J/sWqpaCrh/ropVvmU/wu8y4IpH3uYfmYs4Iodw9R+XeMvxQmYx/TIrubz0MPadblr6TmRsTiEuKTnW0MLaqnxGH9/GzD985Pfb5mc7GFtaSIZd4JYwuFcO4wf2YGzuMXgDlhzK4vnHllCYk8EzWf2Z0PgJDDtTtTLevxc+fghm3uPd35aDx/l/i77izTX7mDGymIsqVMTfMzcTd45gdtlALrvsdDjUC56Yx/eyP+DO17PJtNv42shi8rIdNK5/mwnrHyVH+CLO/3mrhg1yEXnZDp6YmM1UoHrvVu7+bBfvbjzAQ5eO49KJKtNr/d4arvz7p4zuV8Bfr55IQbcMDh1v4rp/Lqfp0A4W2KG+aje5Q4EdH8G2Bawfezc3Pr2dyqP+I3j/nVFIRu06Ll3ju1/OtX3K7zOeZE721znhit8xebCntb55HjKzOy8dGcb9cz6gocWX6fQdexX3ZcC/3lrADQKVNdOth7cVVl3fwveeW8HKXf4R/P/Y3+FXGf/iGeds7p/Xjz9mjGL65neYteZCXNg53baO5zMP8ZNNZby1QZ1jJm5WZOWw7837+XaLkway+ef/nMT0kb1JJImtNkwIIW4AbgAYOHBgVPt4ecUe3lm3nx2H69lztJGRffK4cfpQpvWZQt7yP7HPuYscRzOvbmqkee5GLisWjATmfLSO/UXdye/mID87gwvra2nobqemqo6S/MHkAk0HNrOr+2T+9vFXvL5qL+MHFuJ0SW57ZQ2/fmsDPZsrOTsLSvv25b4PtvLy8j3UNLbyO5HFzOxG/nL+cM5+70MynHX89YI+NOb0Z8qQXpQUZLcph+hdzsm7PwM3XDhtMqf0rvB7v+++w2Qs/y9PnplFVvMRRmz9O+tG38nRnuPYcvA4L6/Yw4JNB7m58BNuB46edCs9Pvg5zp2fcOaJF7Jq5adkZqxmz5Gj3Fe9nONNTj7fWc2Ant24/6JR5Gdn0HNJP3ri5tHTfccuOJYJHwH2LP70wVbsQvCTklxohll5u2jIGImQTmbluMk7uYJBvXIYV1qoIjFXK96MmjzVyWg/tpPCiqt4/OIJuGv7wR8fAuCxxXuZV7WCq6YMouf+RsZ5jn/m4ytpJpP8bAcrRSavLNvIk8dP5B8DHMgjDsYN6QdCcMO0oezNvov+865l3gnvs2HUzznr/Vs4UDgN96g7yPzwPH7TYx7Uw/fOn8o13UuZvGUYmZWfQoadn59dztfH92f93lqymqrIeNfFuAmn8OjgCoR7NK3z/pdbRx7lW1OnMHFQDzL+371QPJKPZk1n9Z5jlOytguXw8Bn5nLB0D1+OvJFHy9X3mJ1hZ8LWyWR/+QYjhx6BnfD9Ky/39fsAzvdOwvbpch69eCwIG0LAsN7dKS/JV8FKILuUzXjnN2cyuv4EVu85xv1bvwuui3jm699VLbhDm1Q/wYjZuPtN4L63NvDcJ7volmHnO6eWccvMYaoi9WBztZKX62kh9T4BRpzDt/e8w7Dv3MmJg/qqVt+KZ5CbHuJ4jxNZUfZtQNCakc/3+kzDDby4fA+/W/YV72TBb194jw+dkxnZJ487XltLYbcMhvbuzrXPfE52hp3lO6u5/K+f8MsLTuSO19ZypK6FGcOGwQ545p2lLFtbzrX1czgDB5d+PpzBfTN48JJhZDl82Sx9vziBkoOLePTrFQh3K6M2/IFh258DYFLLCs772ydcXNGPcQMK+caXi9ltK+fON7dw+rAiLpnYH4Eqf+me3bAKRmcdoKXZzh8WHuD27ELsh7ew+0gD3/nH51Qea+Sec0+gOE+1KMt2vEjF2n+xr++Z9Jr0ex61Oei39xv0XLGEf86SHOlVwWlLH6Wxrjdnnn89Z5jszM37fstJy3/GR6V/49OTn+CEvvltf+M4Ew9h3wuYjeJSz2t+SCmfBJ4EmDRpUlSz7ew71siB2mZG9Svg7FElLNh0kB/9+wum2LrzYqabF06rgs+gfMggblmygyViN/Oz4PPNO5jr6o3L4xmekVXL+zXHuXvjR4BkdVYub8//gHucZdgE3DprOD+cMQybELyz/gD/Wb2XK/pLWAzfOaOCEzIm84f3t1DcPYtZ3U8gb/0KzpeLwKmmcj27dy0Mnxy6IMXl2DzDz0+bUAHF/f3fHzILlsPXNv3KO0Xr1zbdBzcuhvH9uXXWCN5Zv58eb/8/DspCps3rzZrMDO4aXcOAKydS8+678An0de7lUE09LW4bd59bzrWnlvlulK394NAmLh5vOvaevfAR3HF+Bd/rNw27TVCwvQVegdyGvTB+JtTuo6DxqP/nwJfZ4shUuewGfZVs2/JLVCfVsV3cNGsUv/jwMAs2HeJnjuOMc4AbwS8uGk+f/Gze3XCQ2g3Z5MgGXvjeyZy6+UOoL/B1pAH9J18M1Tcz9NMnGJrbDM1HKDnrp5QMPR12Tqf79kWA4Kwp45Udta+XX1N7WO88hvXOg2NueBcqynpTYZRp/UkMaVzHkCGerKe6gzB4GoN65TKoVy4UDoflMFWuANyUTz6T8qGm7+P4SFhTowYm9RruJ+oAjh4Dwd3KxcPsPt+8PTw57N2LB3LFqIFcMXkgWw4O5qxHPub5T3fxozOGw+z/gx0fId/4PncUP8Erq6v4zqll/OiM4f7Wnfn3MnvPp9+KeOZsTql5B5rPgfcfglXPIYafRf6l/2BSVvc2u7i4oj+vLusOC6Air5YfXDOV3vnZXPX3T/nBC6vomZuJBF66YQr7jjVx4/MrueqpzyjqnslL35/C2NJCnA8WMSmrkY/dbobWrWKzo5z7Lz2JSyaUtq3kjp8Iu1/j4ua34PO/qY7ck28Em4MTP/srt0zrz9+W7ueD1du4NmsrC+Wl3H/RKL598iA/G4jcIbAKpuQfpramF39bvINBjjrOchzkvD8vxm4XzLn+ZE4q8/xuXzwPa++HEefQ7/LnuMiwu064DFbdwVT3cujZGw5/DrMf4MJJg/3Pe/x1MKA7xa/fwAWbfw4VcUh06IB4CPtyYLgQYjBK0K8AvtX+R6Lj1lkjuHXWCO//d8wu572NB1mwrhj3V9mUHVSjvC6YMpqi6VNoPVIC8+DRi4fw6IRzaGhxcayxlZ6Pu5g2ZBCPlI/jUG0zx5cPZabjKI/NGM+J/fIZWuy7iM8b25fzxvZVnSSLgexCTh7Ui5e/7xnwsHih8uw/eUx1ah3eojoah88KXRAjvQp8g5PM5PdT4nhkG0y9TXU8vnSVGhz0tdvJdNi4aEwf5Px1HBg6i3OzynAdHc+AOpUfX7DjHUDgwMlbV/X3DcAwE2yGRKODx5HpEwOz3953nPJBDwXpPnGaOl49Ebv3MwYDToZju7h8yggmj8tmf00TFTvWwhKwZXbn6lPKADhrVAnyT724qDQPMbQIVgcMDDOYdR/sXALrX4Xeo9ScIgAnXa9S0fJKfOKV01PN0+Ns8fehjQrJ3GE8cIqyNZqPq7+mYz7rDnzplpvnqjRKI9fawPi+K5erXOZACgz7b0+Ywu7pXDRtO6JPHjNGFvPcJzu5YdoQsrsV4pp1P/bXv8vOfYv56ZkXKsEPReCCKgOnqEE8H/4vvHs3IOCUH8KsX6tOwCDYbILLTx+D/LSEbw86ivDcN//4n8lc+tdlHKxp4sUbTmFIcXeGFHfnlRtP4ZklO7hl5nAG9lLJC47CUk7JbeKVS06E32+HabczZtKAoMfzpjzOv0PdE1e+BCNnw5fvID75Cz8b1cCPzz6bxk3vY3tV8p3LLyd/VFnb/Xgy22zV2yksGcuzl00m5+P36FH5MTPLi7nljBEM622qyD78rUpnvfxZ/2snOx8GT1UV+MGNytKZcG3wcx97ubpH3rxFzfR54kXBt4sTMQu7lNIphPgh8C5gB56RUoYxg37s2GyC2aNLmD26BJ47RXl0ADk9OWVwL+jvgHkgmo+DEORmOcjNtIOzgdLevSgd7xHVmgrY/DYXjGvnJjOGIAcKjDFY5thu+MZTMP/OjufxMKYWyOnlS7s0IwRc8YISJWOek1HfUGIz6utKOPatQjQdo++E83hkdAUsOB2W/Vk1yQ+sVdtveF3NSxNU2D0TabldvsEb3qyYgAFKBn0rVEZM3UH/z4G/QGYXqMyA1kbfcH5QKWD7VkF2PmW5GZQV5cIBjx0Q8D2ILNOUy001vv4SM44suPQf8Pw3YMZdvoh+xDlqrn1zpWleYKG7yd80BvmYxWvAyWrel20L4KPfq472E873/+5ARYwlY33ZMga9fJ3w3pGTZgrNuexhdEcd369SMQO+g+9NG8K3/v4Z//liL9+YUMovV+XxAPDjUY2c3p6ou90qD94eEMlPvxNevhYmXQen/Th40BEEMewMlYHiuSZ65mby3x+cRl2zk74Fvo7yE/rm89Bl4/w/nN9fZbrsWqa+88FTQx9o2Jkw5QdKzMum+n7vUk/reM9nOAadSl7VKhA28odOCb4fI7PN7YTuvfnaiGKoGgKVLv70jeGq385MS73KbDJ39BuMPBfm3aaCsFm/Dn4/G0y4Wu2nT+KTBuOSxy6lnCelHCGlHCql/G089hkxQ76mLgzwpTtm5gHCf74YZ7PazvwDFJerXv32hqgb+2iT7uhprncvUbVw8ciOZ94zRrq1d+P0n+ATdYDZD6hRh69eB2tfVgM4hM0XpQ6coi7UBfep/6fdph5D5TrnemamNKd4mSJ2L0bELmxqHpT8vur7qw9IGfRaMVnqhssrUQJnvklOuABuWelvARg3i5ERY1BcrlI4m2rbTuVgpmgY/HiN2reB3QFXzIFzf+97zRD2wFz2YBF76SRAwOvfVzfsFXN8lTGoa0B4bp2BQcSjcKCvciwNYslFOkjJyGEX/tbEKUN6Mbp/Pk8u3s7Nc1bx4uZWGjN6cnr3dibWAn/bzMyQ6XDnLjj3obBFHYBhZ6jryJSim7d3MX23vtjxZ/P7qfLtXKyutcDWj5nsfJj9O9VZbP4ucnspy8sYDLbnM9WCyw7hZZvHohiVvKEZwcY6BNpWZow5aLr1UOmyHdEJog6pNPLUPAjB8DRttrYr3htzLmeYhMQYPNKeIDeFiNhzi9XjSderG8UQ9vbyenOL1OcCc9jbI68PXPAn1TJ4/Xvw+ZOq9jfKatwQW+Yr+6PPKDWyMNQyakaFZK7MvMJusl8MgSoaqSpDwz8PHKTkDBDIcVeqyK8jQgn7lBvV4JVVz7Yv7NBG8ABVMRqzZYJP2ANzlb0Ru7mJXaC+P3crXPqMr/I0sNl9+xsQJOK22VWud2Z3/wrBIKu7+ny4A3tq9we1bIQQfG/qELZX1bNg00F+c9Foug0cr0b7tkewyiwWhsxQFd02z5gKtxvm/hTm39XxXP75/dS9tWU+DJgcPCoOhwEnK0F3OdWskAPa6eMyB2eGxRbq+oC2tpWZwgEw4Ro48/62Lbck0mlZMQmnb4UaOt5c46t9wTetgIGxyIZfxO4R9sNfQtlpwfffVKPmdckIaGqVToJzHvINpigaqS7UukP+ufOBfP2vviHq4TLq62p49IF1asSpOVrM6emZHGqzL3otHhE6Yg82z02wG9640fp6pgUw/PPa/f7CGTi46Wu3h1cmoxLJCBD2/hNVc/uTJ9R5tRfJhUOo+WLchrAHRGTn/F4FAcPPDLE/z/J85smlzJxwgTqW2a4yE8mI59p9IS2Kc8f0ZcGmQ0wfUcwlE0uhfiwse6ztZG5mglVmsZDTE/pPUtbVjLth+0Lf0P99X8DAduwmo2VQvR3GxdA1N2AyrH5eLQjfcjx4S8rAkeWxCht88zSFvD5cIF3tf1eelOKuROoIu82u5r3Yvsh/ZGPgRGDeiN0k0AWlSljai9gbPfPEBEaHNjucfIPvf3Ml0Z6wD2unc7U9jBkg+1W0fW/gFI+wezpmisth5T9VBGULaJwFm28l2FwxxoRdxnwvoSL2aKPAUBE7wGm3whzPKj/tRezhEDJiD3HeoSp4g9xidS0V9A/+vimfPCjFI1WHfGBnbiBul/quQ3SyZthtPHalqYItGassuUObgl8jEP+IHdT1vOj/VAtw+dO++Vh2LW1f2M3las9f7wij5bT0z57/24nYQZ1fa4PJiumoRRfCiumipI4VA6oD7fxH/F8LnJM9mLAL4YluO7BiAv31YBSHYeskilNugXMf9s0lUjRClTdYZGh0APpZMYb3aqoYew5RzUyjRZLbWzW7A6YV8H02UmH3HCtYp9OwM5RXCnEQ9hAearQiN/0OOO+P0Z/P2CtUpfrl2+1v52xWNt/AU8Pbr5GFdKAdOybY1BGxMmwWIOGLf8GWd5QNV1yuOkXbwxD2jFzoNyH64xeNUNfI3hXKXjEWAQmFcS97rZg4Xx9JJrWEvWQMjPum/2uBEbsxhWagkBR10OkZOAFYKPL6qsokGcJeNAwmf8/3v9FJG8xnDzYzZbAbXgiVIWE0Ve0OJe5tIvYgGTXhYBwrs22etDr2j9TzWIU9K09NsRCviGzwNBhxVvTnM3SGsmNW/rP97TJzVCdwe+mzZnoMVkkD7fns8bZiQNlyOb1g4e9U/9LE78CgU1UHeHtLGOZ5hH3glMiDAjM2m6+jesDk4P0uZox7uU3EHrDMZSK+q04gtYQ9GIEee7DOU1CR9vF9oZeyMqyYjhBCRQ+xrnATD7ythyDn4shU3405Yg+2EEYwjGl5zURtxRgee4g0sdGXwLSfw8hzIttvIEJ45gPpIhGZza463bYvin4tz6D7tUHJ6A4idqPMcbQXbDY1cZerBYafpaYwHnSa8rsPrgv9uYxsNftnOBklHWHYMcE6tAPpFiDsjkwVXIS8PrQV07VoE7EH6TwFkzceIoukqSY8KwZUpBxqP51JTk9luYRqPeT08o/Ya/eq1zqKnPL6JsCKCeKxg7qhZv7CN6dPLARM9AQkNyKruErZWquei+9+S8bCgfVtV4Iy8GY/RZmBEorhZ6vHk65Xj4M89lFHdsxFf1GLYcTKsJkqwWHIjI63zS5UwYS5pRj0+tBWTNckcLGNYB47tF1oOpDARTbao3iEGsQTz8Vxo6W4PHSZzPOKg0q/CycFs92IPUKx8HaeBrFi4k23nu14qEmIyAr6KzH84vn4rpjVd6xaYCLUQhyJ6hAcfQlc967Posrvp6yhjoQ9XvSfCHftUS2Wjhh/lcrgMVs2Xa3ij4HUF/bAxTYMYQ+MEAsHqR8vmG0hpceKCTNi9+bFd4GovXiEytAJllefU+S/WEXNHt+oyPbI66siffMc0zFnxbQzYi9edOsRxENNckQ28VqoPxTfqN3IYDJWvAokUWW22dqmGQ46TWXGuN3xPVYozMsutkfZ6XDqLf6vmWZ49KKtmC6KEWUb3rnReRp4AdgdavRaMAulpV7lsoZtxbTjbXc2xeXKRjIWFTCT08sXsUvpidjDsDzyjZRHkx0TbNRqOBgtp84Y3JHTM4iHmuSIbNiZKuPl7Z/C/LvjE7kXl6vyhPLZo21dRUPZaSoK7gr3QkdoK8ZCZJkW24DQVgyEHtATatRpKAoHKu+4K/js3tV2gtgxuR6PXUpPBN4YfsQO/sIerVgU9IeLnoATL47sc9HQ7o2bpIjM7oBr/guTv68Wzfjn+WrwVyw4MtWI11CZMZ1ZZq/PvjTxx4qVrljxR0nqC7sxX4SRy95Sr0Q32IjAfuOVPRHY6eRdczPMiN1mVxd0V2i+FZerhS8C130FVVZXi5rB0FhpPlyPHfx99ljEYvxV4beGYqFbD1Wxm5dBNM7blsTfypGpUhoveRrqDkCbdXuiYOCpoTONOjMKLRykrKFOXhouKoyK32wbuaJsiSaZ1Bl5GgpDjI1IrbUh9AV/2o/VXyChZnZsj6vfCH/bRJLfF34UYv1U7+jTwz5hjzZiT1SmRTzx2nI1vtHJXSkiG3OpmkguHgHBOQ+Efs8oc2f8VkKodQSsQLeeaoK75lpfoKGtmC6K4Qcbc1q3NIROrQuFYcV0RlTZmXgnAjviG50aTlpht54qwvWL2A2B7MLCbqRWugI7fUXoOV06m85o5Xnnzu8CLcquRLBpBfSUAl2UvL6AUItVgydiD7Pn3MBrxcQ4+rGrkWOaL+bYHjViMRy7yWbz5LKbhb2ZLiWQwTAiVPOMg65WFY11NFIxlbBoFJpwgk0EZtHvKvWF3Z6hRMizvFi7VkwovFZMikXsuaYZHo1Ux3AFLreo7ZS/xlzsXRXj5vSL2Fstd9PGTFeyn7oSxkIm5tHnWti7MAX9fRF7LFZMqkbs9YfDH5xkkJnryzACawikN2IPsGIs1syOGYuKVcIxrg9XQIsOLHeNpIew55uEvbU+8ojdWJqtK9sM0ZCZqzzxhsNQszu8jlODjBzf9AygouCuLhTeiN1847aziEKqkojZHVMB4/uIx8C7JJMewl5QqqwYKT0RexRWTKrZMKBsk9witeZkU02EEXuOf8TubOnaGTEQImK3QEsj3mgrJjjezvWAih8s912lj7A7m9Rw4daGtjM7dkRHS7NZmZxesM8z9DyiiD3XN4oXrGFp2IM1tS1w3vHG1aKmMA5cfCXdcQSL2LUV03XJ96xyU1sZZVZMmItsWJHcImXDQMeLE5jJzFG2loGruWunOkKIGzcNrRinBWyzZOCt+LUVYw2M5ctqKmOwYlI4YjeIxIrJyAmI2Fu7/ui8oDduq+WisZhJxzKHQ6jOddDC3iXJ9yyYe2yPmg8lKismRSN2IzPGnqXW8QyXzFw1a6bRVLVCFOiN2NO98zQNyxwOofpgQFlXFiI9hD23WF3IR7aq/yON2FPaivFE7AWlkXmuRmaRkRnjaun6Vkyopna6iZyrtev/VskgZB+M9QawxSTsQoiHhBCbhRBrhRBvCCG6pvrZbGrSf2O2xUjSHZ0typdPWSvGE7FH0nEKvsrRyIxxtXR9KybkyFNrRWMx42rWVkww7A61olUKZE3FGrG/D4yWUo4FtgB3xX5KCSK/FA57IvZIhD3SmR2thuGxR+Kvg2/FI8Nnt4IVE3TkaTpG7GlY5nCxZ/lfH1a4roMQk7BLKd+TUhpLkH8KlMZ+SgmioNQ3t0kkVkyqTgBmYMzwGOmaokbl2Gq2Yrr4DRDMQ3VbMyKLCSt0dCcLR2ZKZE3F02O/DngnjvuLL0ZmDETWeZqqE4AZFJQCAoqGR/Y5o3JsMVkxXf0GCDryNA0zRCwahQHHpQQAABLzSURBVHYKjuyUsGI6NBeFEAuAkiBv3SOl/K9nm3sAJzCnnf3cANwAMHBgHFacj5R8k7BHErH3HAJX/Bv6TYj/OXUFCgfCTUuh+ITIPmdUjkbEboWRp0KomzQFIrKYSMcyh4s9KyUGsHUo7FLKWe29L4T4DnA+cIaUwVZM9u7nSeBJgEmTJsVhiZgIKTC5RJF47Dk9ofzc+J9PV6LPqMg/0yZit0gUaM9KiYgsJrQVE5oUsWJiSgcQQswGbge+JqVs6Gj7pGIW9khnd9S0JWi6owVuAEdmkM5T60VkMeFq6ZzFw61I0IrfetdHrB77X4A84H0hxGohxF/jcE6JwWzFRDqlgKYtmRa0YsBz4+oBSmlX5nAJWvFb77uKKWKXUg6L14kknOwClaLXUhf5yFNNWzIsasW0uXHT0YpJw1ZKuLTpPLWmsKfHyFNQHWeGHRPpyFNNW7wRe4Na1d3ttMYN0KapnYYi57JI6yoZ2DNTImsqfYQdPHaM8M27rIkem12JZEu970awQoecw3TjSmnZiCwmnGlYmYWLI1jFb73rI72EvXCA6jSy2LwPXRZjsQ3vDHgWiALNEbvbM7Yu3UTOomLVKbRJh7WmVZdek2Sc+iMYdmayzyJ1MBbbsNLUpg5TnrKVzjueWFSsOgVHVkpkTaWXsPcaqv408cFYbMOIcKxgxdgzofm4em4Iu816N25M6Ig9NI7slMiaSi8rRhNfMgMjdgtYMeaIzKLLnsWMVTKYkoE9SNaUFQKWALSwa6InIzfAY7eAQNozfRFZOi7q7HaBdKdXmSPBETjOwZqVoBZ2TfRk5qisGK8VY7WIPQ09ditlMCUDe6Za+N5AWzGatCPDyIqxUORrHnmajlaMUQlb4bdKBo5sVfEb017pPHZN2uH12C0kFuaRp2kZsVuoEk4GRkvG+J50xK5JOzICs2IsYMX4RezpKOwW6g9JBuZ1ca00ojoALeya6MnM8UTsFooC/SL2NLRirJTBlAzMq2y5rXt9aGHXRE9GrhJJY0FrKwi7sZCCMZ0AWOO844WO2NvHuBaczZa+PrSwa6LHmEzNWBfWClaM10NtsfSNGzXpWOZIMOaRcjVbqyUagBZ2TfQYU/c2HlWPVogC7aamdjpbMVaohJOBUfE7WyzdutHCrokeY+reRk/EbgXf1hC0dI3YndYVq07B3Hlq4etDC7smegIjditEgSnioUZNOpY5EhzBWnTW+660sGuiJ9OCVozDHJEZN24azYVnYbHqFIJW/Ba4rgPQwq6Jnszu6rHJQlaMPZiHmkYil45ljgS/zlPrflda2DXR06bz1AI3gDlid6dh9GqlUcLJwK/z1Lg+LBCwBKCFXRM95s5TmwNsFricvFkxLWmaFZOGlVkkmDtPvfPqWO/6sMCdqOmymCN2q0Q13jx2aze1o0bP7tg+fp2n1r0+tLBrosfoPG2ps05UY0+NGzdq9OyO7aOzYjRpT0au77kVUh0hYOSp58a16awYjQd7sHEOFglaTMRF2IUQPxNCSCFEUTz2p7EIdodPIKxixQRG7PZMECK559SZWFisOgVHaoxziFnYhRADgLOA3bGfjsZyGD67VYTCb+RpqyVv2pjQszu2j7fib7J053o8IvZHgNsBGYd9aayGkRljFSsmcACKBW/amNARe/vYzVZdmkbsQoiLgL1SyjVhbHuDEGKFEGJFVVVVLIfVdCW8EbtFLn5HwFwgVjnveOFqAVtGetlPkWCzedY9tbYV02GvkRBiAVAS5K17gLtRNkyHSCmfBJ4EmDRpko7uU4VMiwm7PWAAilXOO164Wq3TukoWxpz9FrZiOhR2KeWsYK8LIcYAg4E1QtX+pcAqIcRkKeWBuJ6lpuuSYTErpk3Ebr2bNiaczelX5khxpEHEHgop5Tqgt/G/EGInMElKeTgO56WxCpaL2M0jTz22RDqRjvZTpNizLC/sOo9dExtG56lVLn67A4TNE7Fbc6HimHC16oyYjjDWxU1lKyZcpJRl8dqXxkJ4rRgLCaQ5IrPgTRsT6VjmSHFkW36cg47YNbFhNSsGPBFZS3raEq7m9CtzpNitf31oYdfEhjfd0ULNe2/E3pp+0Ws6ljlSHNZv0Wlh18RGpgWtGEeW5SOyqHG1WCeDKVn4WXXWvD60sGtiw2oDlMB/AIqVzjseONOwzJFi7jy16HelhV0TG5b02E0DUCza1I4aC9sLnYYj25cOa9HvSgu7JjasNkAJAjxUC1VI8cDVYq3+kGRgNyJ2614fWtg1sWHFiN2eZfmmdtSkYyslUhxZvtkdLfpdaWHXxEaGxQYogWfIuLWb2lGj0x07xm6+Pqz5XWlh18SGEbFbyYrxRuzWvXGjJh3LHCmObMtfH1rYNbFhtYU2wNPUTufZHdOszJHid31Y6Lo2oYVdExveuWKsFLGbO8fSaL1T8MzuqIW9XXTnqSbt6TEYJn8fhs5I9pmEjxGRudM0Yk+3MkeKIwvcTmhtsux3lWbhiibu2B1w7u+TfRaRYc+E1gaQbsveuFFj4Si00zC+n5bjlv2udMSuST8cWdBSp55b1EONCim1sIeDI1s9NtdZ9rvSwq5JP+yZKk/ZeJ4uuJ2ATK8yR4PRudyihV2jsQ7m1EyL3rhR4V0RKI1aKdFgJAJYeJyDFnZN+mHO4LHojRsVhrBbacxBMkiBil8Luyb9MOdxW/TGjQqnjtjDwnxNWPS70sKuST/s1o/IosLCizN3KkbnKVj2u9LCrkk/HNaPyKLCK+zaimmXFGjRaWHXpB9pG7G3qsd0qsyiIQX6YLSwa9IPh/Vv3KhwNavHdKrMokF3nmo0FsRu/aZ2VHgj9jQqczSkwPWhhV2TfpgjMls6RexGuqM1xarT8Os8teb1EbOwCyFuEUJsFkJsEEJYbNIQTVqSAhFZVDi1FRMWKdB5GtMkYEKIGcBFwDgpZbMQond8TkujSSBp67FrKyYsUqBzPdaI/SbgASllM4CU8lDsp6TRJJgUuHGjQuexh4e54reobRWrsI8ApgohPhNCfCSEOCnUhkKIG4QQK4QQK6qqqmI8rEYTA2mfx25Nseo0UiArpkMrRgixACgJ8tY9ns/3BKYAJwEvCyGGSCll4MZSyieBJwEmTZrU5n2NptNI14h96Ay44SPoMSjZZ9K1SYHro0Nhl1LOCvWeEOIm4HWPkH8uhHADRYAOyTVdlxToHIuKbj3Un6Z97A4QNs9CLNZs0cVqxfwHmAEghBgBZAKHYz0pjSahpMDIQk2CMa4Ri1b8sS6N9wzwjBBiPdACXBvMhtFouhQp4KFqEowjE5yNlr0+YhJ2KWUL8O04nYtG0zmkax67Jnwc2UCNZVt0euSpJv1I1zx2TfhY3IrRwq5JP4yb1ZYBQiT3XDRdE6OD3aLCHqvHrtFYDyHUDZtO88RoIsMbsVvzGtHCrklP7Flg0w1WTQh0xK7RWBBHpspV1miCYczwqIVdo7EQ9iztr2tCYwi6tmI0Ggth0cmdNJ2EkTll0fVhtbBr0hN7FqDH0mlCoCN2jcaCODJBD5LWhMKRbel0WC3smvTEngXSleyz0HRVHFmW7TgFLeyadMWRDe7WZJ+FpqviyLKsDQNa2DXpyik/UNOyajTBqPg29Bmd7LOIGi3smvSk/Nxkn4GmK1M6Uf1ZFD1CQ6PRaFIMLewajUaTYmhh12g0mhRDC7tGo9GkGFrYNRqNJsXQwq7RaDQphhZ2jUajSTG0sGs0Gk2KIWQSJkISQlQBu4CBwO4wPlIA1IS5+2RvG26ZEnX8RJXfKr9VIsqUqOPr6y/1rr9Ito3mtxokpSzucGspZdL+gKowt3sygn0mddtwy5TA4yeq/Jb4rRJRpi7y/evrzwLff1f4raSUSbdijoW53VsR7DPZ24ZbpkQdP1Hlt8pvlYgyJer4+voLH6tcf5Fsm6jfKjlWjPfgQqyQUk5K2gkkgFQsE6RmuXSZrEMqliuRZUp2xP5kko+fCFKxTJCa5dJlsg6pWK6ElSmpEbtGo9Fo4k+yI3aNRqPRxJm4CrsQ4hkhxCEhxHrTa+OEEJ8IIdYJId4SQuR7Xs8QQjzreX2TEOIu02d+LIRYL4TYIIS4NZ7nGA0RlitTCPEPz+trhBDTg+zvTfO+kkG8yiSE+KYQYq3nt3owCUXxIoQYIIRYKITY6DmfH3te7ymEeF8IsdXz2MPzuhBC/FkIsc1ThgkB+8sXQlQKIf6SjPKYziNu5RJCPOi5t9YLIb5poTKVe67NZiHEbUH2ZxdCfCGEmNvZZTGdQ9zKFLMGRpJCE0ZKzjRgArDe9Npy4Gue59cBv/E8/xbwoud5DrATKANGA+s9rzmABcCweJ5ngsv1A+Afnue9gZWAzfS5bwAvmPdl1TIBvVB5uMWe954FzkhimfoCEzzP84AtwInA74E7Pa/fCTzoeX4u8A4ggCnAZwH7+5Pnt/pLkn+ruJQLOA9433Nf5Xp+73yLlKk3cBLwW+C2IPv7qee3mmuh3ylomYiDBsY1YpdSfgxUB7w8AvjY8/x94BJjcyBXCOEAugEtQC1wAupCbJBSOoGPUGKYNCIs14nAh57PHUKlNE0CEEJ0R12A/5vgU+6QOJVpCLBVSlnl2W6B6TOdjpRyv5Rylef5cWAT0B+4CFXp4Hm82PP8IuA5qfgUKBRC9AUQQkwE+gDvdWIRghLHcp0IfCyldEop64G1wOxOLIqXSMskpTwkpVwOtFmoVghRiqq0nuqEUw9JHMsUswZ2hse+AVUwgMuAAZ7nrwL1wH5U1PewlLIaVVNNFUL0EkLkoKKPAXQ9QpVrDXChEMIhhBgMTDS99xvgD0BDZ55oBERapm3ASCFEmaeCvpgu8lsJIcqA8cBnQB8p5X7PWwdQgg3qpttj+lgl0F8IYUP9Tm2a/MkmlnKhfsfZQogcIUQRMIMu8HuFWab2eBS4Hegyi9jGWKaYNbAzhP064GYhxEpU86TF8/pkwAX0AwYDPxNCDJFSbgIeREVK84HVnu26GqHK9QzqRlqBuuCWAS4hRAUwVEr5RjJONkwiKpOU8ihwE/ASsBhlpyX9t/K0jF4DbpVS1prfk6qt21Eq2M3APCllZYJOMSpiLZeU8j1gHur3+zfwCUn+vWItkxDifOCQlHJl4s4yMuLwO8WsgQlfzFpKuRk4C0AIMQLVZALlsc+XUrYCh4QQS1HN++1SyqeBpz2f+R1KVLoUocrlaTr9xNhOCLEM5bV9DZgkhNiJ+t57CyEWSSmnd+6ZhyaKMiGlfAvPqDghxA0kXygyUDfVHCnl656XDwoh+kop93ssiUOe1/fiHwmVel47BRUx3Qx0BzKFEHVSyjs7pxRtiVO5kFL+FuXpIoR4Ac/vmAwiLFMoTkO1Js8FsoF8IcTzUspvJ+7MQxOnMhGrBiY8YhdC9PY82oBfAH/1vLUbmOl5LxfVybM54DMD8XU2dilClcvTzM31PD8TcEopN0op/5+Usp+Usgw4HdjSlUQdIi9TwGd6oCLdpPmcQgiBuhk2SSn/aHrrTeBaz/Nrgf+aXr/Gk0UyBajx+KRXyf/f3v27RhEGYRz/DiJBCASMioXoIUQL4UyR0iKNgmCpEARFEARBsTAWVmksrCUR7AQLC/EPCKiNKKnkLkJARdIEgtiIQUzhZSzmPRKO05jcent57/nAFrfsvuywx7D7/ph1P5zu1STRX11mUi8krjRzZDi1WQWqlDSGsI2Y2nL3u+5+KN2rCeBViUm9kJhSW53lwK2MtG62Ea93y8RgwBJwFbhFPBV8BO6zvihqEHhG9OsuAHc2tPM67atT4iyLbcZVAT4QAycviGpsre1VKH9WTCExpXYW0jZRckyniNfceeL1tUb0Tw4DL4FP6fr3puMNmAE+A++BsTZtXqH8WTGFxEU80Tbv1RwwuoNiOpj+p9+JwfslWmb0AOOUOyumsJjoMAdq5amISGa08lREJDNK7CIimVFiFxHJjBK7iEhmlNhFRDKjxC7ZM7OGmdVSpby6md1Oc/X/dk7FzC526xpFiqTELv3gp7uPuvsJ4DRwFpja5JwKsTpaZMfRPHbJXioHMLjh91GiZO0+4AjwhChjC3DD3d+a2RxRZW+RqMj3gFi0NQ4MADPu/qhrQYhsgRK7ZK81sad934DjwAqw5u6rZjYCPHX3MYuPiUy6+7l0/DXggLvfM7MB4A1wwd0XuxqMyD/470XARHrcbmA6Vd9sEDXp2zkDVM3sfPo9BIwQT/QiPUWJXfpO6oppEFX2poAvwElizGn1T6cBN919tisXKdIBDZ5KXzGz/UTVymmPfsghYNnd14BLwK506ApRk75pFrieyrJiZseaFS9Feo2e2KUf7DGzGtHt8osYLG2WVX0IPDezy8RHDX6k/fPEB1LqwGPi+6cV4F0qz/qV9U/RifQUDZ6KiGRGXTEiIplRYhcRyYwSu4hIZpTYRUQyo8QuIpIZJXYRkcwosYuIZEaJXUQkM78BA6rrUIUCytEAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "combined[['Cash Rate', 'Lagged Inflation']].plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not only has the scale of the correlation increased, the sign has swapped! Note, if you choose different lag periods, you will get quite different answers. Further, the economy is much more complex than a single causal relationship - there will be other factors that alter impact of the Cash rate on the inflation, so it is not a single one-to-one relationship."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "Compute the following graph, which has the lag value as the x-axis, and the correlation as the y-axis.\n",
    "\n",
    "<img src='img/lagged_correlation_plot.png'>\n",
    "\n",
    "Note also that there is a spike in the -1 to -3 lag period - what does this mean?\n",
    "\n",
    "Note that when you pull down your data, your time period will differ to the one used to create this image. Therefore, your results will vary, slightly, from mine. If you are unsure of your solution, rerun the provided solution for an \"up to date\" plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c8b6849e48>]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lags = np.linspace(-10,10,21)\n",
    "lagged_corrs = []\n",
    "\n",
    "for lag in lags:\n",
    "    corrr =  combined[[\"Cash Rate\"]].corrwith(combined['Inflation'].shift(int(lag)))\n",
    "    lagged_corrs.append(corrr)\n",
    "\n",
    "plt.plot(lags.tolist(), lagged_corrs, \"-\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/lagged_correlations.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing Cross Correlation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.tsa.stattools as ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "combined.replace([np.inf, -np.inf], np.nan, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "combined.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Inflation</th>\n",
       "      <th>Cash Rate</th>\n",
       "      <th>Lagged Inflation</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1993-03-31</td>\n",
       "      <td>0.8</td>\n",
       "      <td>5.25</td>\n",
       "      <td>1.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1993-06-30</td>\n",
       "      <td>0.5</td>\n",
       "      <td>5.25</td>\n",
       "      <td>1.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1993-09-30</td>\n",
       "      <td>0.5</td>\n",
       "      <td>4.75</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1993-12-31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.75</td>\n",
       "      <td>2.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1994-03-31</td>\n",
       "      <td>0.5</td>\n",
       "      <td>4.75</td>\n",
       "      <td>-0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Inflation  Cash Rate  Lagged Inflation\n",
       "Date                                              \n",
       "1993-03-31        0.8       5.25               1.6\n",
       "1993-06-30        0.5       5.25               1.8\n",
       "1993-09-30        0.5       4.75               0.9\n",
       "1993-12-31        0.0       4.75               2.4\n",
       "1994-03-31        0.5       4.75              -0.2"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combined.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "ccf = ts.ccf(combined['Cash Rate'], combined['Inflation'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0c488b1da0>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ccf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A good rule of thumb is that a correlation is significant if it is higher than $\\frac{2}{\\sqrt{n - |k|}}$, where $n$ is the number of datapoints, and $|k|$ is the lag:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.0, 1.0)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = len(combined)\n",
    "x = np.arange(0, n)\n",
    "threshold_positive = 2 / np.sqrt(n - x)\n",
    "threshold_negative = 2 / -np.sqrt(n - x)\n",
    "\n",
    "plt.plot(ccf, 'b')\n",
    "plt.plot(threshold_positive, 'r')\n",
    "plt.plot(threshold_negative, 'r')\n",
    "plt.ylim(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see \"significant\" peaks at 20, 36 and 40. I put significant in quotes here - this is just a rule of thumb, and should be tested more robustly. Further, we haven't checked our assumptions about the data that are necessary for such a test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([19, 63])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(ccf > threshold_positive)[0]  # np.where tells us the index where a test is true."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([40])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(ccf < threshold_negative)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Requirements and assumptions\n",
    "\n",
    "Cross correlation tests have important assumptions that must be adhered to.\n",
    "\n",
    "* No autocorrelation\n",
    "* Time series are stationarity\n",
    "\n",
    "We will examine both of these concepts, and how to test for them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Autocorrelation\n",
    "\n",
    "Autocorrelation is the rate at which a series of data (usually time series) correlates with itself (specifically, itself with lag). An example of this is a time series where one value is dependent on the previous version:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here is a completely random series, it should not depend on itself, and therefore should not have any autocorrelation\n",
    "random_values = [0]\n",
    "\n",
    "for i in range(100):\n",
    "    # Just a random value\n",
    "    random_values.append(np.random.random() - 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c8b7d6fd08>]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(random_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\marin\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\stattools.py:541: FutureWarning: fft=True will become the default in a future version of statsmodels. To suppress this warning, explicitly set fft=False.\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c8b7f13508>]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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h1NtU1tTxz9X7AfjVf7f3qvScOpWtAn7DRua661XLqmrreOCdDUSFuPjVN8YhIgzvH87Q2DAWbrYu4G/Oc9e6BwcG9Joe/rr9RQzvH05USGDjscsmJuAIEN5brzX53izYeIDCsmqunpLExpxj/GeTpr96M1sF/LCghn1tNeC35OnPdrPj0HF+f+V4osNcAIgIc8bHszrzKAWl1qxsvSm3mIhgJzOHxrDrsO8Dfn29YV12UWM6p0FMeBDnjIjlg/UHtPfajDGGl1dkMSougt9dOYGxCZE89vFOKnWToV7LVgE/pHFfWx249SYju4jnv9jLNWlJXDB6wEmvzR4XT72BT7YetuRam/OKGZ8Yxaj4CPbll1Fd69s02978Ukoqa5k8qO8pr12emsihkkpW7dOlFppanVnI9oMl3DojGUeA8Milo8k7VsFLKzJ93TTVAlsF/LDGfW21B9JceXUtD767kfioEH56WfM96GF0fARDYsL4aEvXyzOrauvYfrCE8UlRjIyLpLbesDe/tMvv2xUZ2UUAp/TwAS4aM4DwICfv6eDtSV5ZkUXf0EC+kere0XTG0BguHD2Avyzda9k3QV85WFzBhU98wccW/H/vTWwV8EN0E5QW/e6jHWQWlPH41ROICA485XURYfa4OFbuPUpRWXWXrrXrUCk1dYYJiX0YFRcB4PNB0XX7i+gbGsiQmLBTXgsOdDB7XBwfbzmk4z8eOYXlfLLtENdPHUSwZ2wM4OE5o6isqePJT3f5sHVdNz89lz1HSvnhu5vIKSz3dXMsY6uAH9aQ0rHZ8gpLdxzhO//M4OcfbOHZpXt4Nz2HZbvy2XGohKKyapbvzue1r7K5bWYyM4bGtPg+c8bHU1dv+GRb1wZvN+a6B2wnJEUxJCaMQIf4fOA2I7uIyYP6IuJti2Z3Wqe0qpZPt1uT0jrdvb4qGxHhpumDTzo+NDacm6YP5s01+3vF2ExnGGOYvy6X0fGRAHzvrfXU+EllnyUboJwuQm2Y0qmvN/zyP1spKK0mQKCk0vuHXUpsGD++ZFSr7zU2IZKB0SEs3HyIa88Y1Ok2bc4tpm9oIEl9QxARhsaG+7Q0s6ismr35ZVwxOanFc6an9CM+Kph/r89j7sSEHmxd71NeXctba/Zzybg4EvqEnPL69y4Yzr/W5fKbhdt55bapPmhh16RnF5F9tJw/Xj0RlzOA+95cz5Of7uJHbfx8NDDG8PbaHKYM7svwARHd3NqOsVfAD2oYtLVPwF+2O5+so+U8fd0k5k1KpLKmjiMlVRw+Xun+vaSSYxU1XJGaeNJXc28aqnX+vjyT4vIaokJPTf20x6a8YsYn9WnsTY+MiyA9q6hT72WF9Tkt5+8bBAQI8yYl8uLyfRSUVhETHtRTzet13luXR0llLbfNSPb6enSYi++dP5xfL9zOsl35zBoR27MN7KL56bmEuRzMHh9HqMvJl7sLeO6LvcwcFsPMYS1/Awb3hMKH3tvM/IxcJg7sw7+/M6PFb42+YKuUTmhgQ1mmfVI6r67MIjYiiNnj4gF3PnpQv1DOSI7m0gnx3H7WEB64aATJXnLX3swZF09tvel0aqOypo5dh48zITGq8djIuAjyjlVQUlnTqffsqnXZx3AECBOSolo97/LUROrqDf/ZaN9ac2MMr6zMYnxiVKsfkDfPGMyg6FB+s3D7abXaakV1Hf/dfJA54+MJ9aSAfz53DCkxYXz/7Q0cbWUwurKmjnv+sY75GblMTY5mY84xVmf2rtnH9gr4Qb1v0NYYQ1lVLQeOVZB/3NrKhqyCMj7flc8NUwfhclrzTz0hKYrEPiGdXkxt28ES6uoN45sE14aB210+yuNnZBcxJj6y8Qe8JSPjIhgTH8m/bVyts3x3AXuOlHLbzORWe65BTgcPzR7FjkPHeTc955TXK2vqWLYrn98s3M7tr6xtrJLytUVbD1FaVctVU06k90JdTv50/WSKK2p48N2NXudjlFTWcMtLa1i84zCPzhvLa3dMpV+Yi79+sbcnm98mW6V0XI4AHAHik20OjTE8tmgnuw4d51hFDcfKqymuqKW4opqaOvd/oCBnAGt+cmGnUyXNvb4qG4cIN07rfL69uYZqnde+yqaksoZILxU9rdmUc2LAtsHIOPfg2I5Dx0lLjrasre1RW1fPhpxjXHvGwHadf3lqIr9euJ29+aUMjQ3v5tb1Pq+szCImPIhLJ8S3ee7scXGkDe7LHz7ZxaUT4sk+Ws7y3QV8uSeftVlFVNfWE+gQwoOcfPPvq/nbzWnMaCNl0t3mZ+QyKNr9DbipMQmRPDJnND9fsJWXV2Zxx1lDGl/LP17FLS+tYdfh4zx1rTt1CnDrjGT++OkudhwqYZTn/7iv2aqHLyI+WyJ5b34Zz32+l735pQQHBjAqLpKLxgzgW2en8NDsUdw9K4Wq2nq2HLBm1cGyqlreSc9h9vh4+kcGW/KeDWaPj6e6rp7FnUjrbMorJiY8iLgmbUqICiYiyOmT0swdh45TUVPH5FbSE03Nm5RAgMBP/72FTZ5qo97ipS8z+bgbVjVtkFlQxpIdR7hx2iCCnK2P94D75+2RS0dTUFpF2v99xmV/+pLff7yDguPVfHP6YF6+7Qw2/vxiFv3PLAb2DeXWV9ayZIfvqqDyjlWwYm8BV0xOJCDg1G8vN585mAtHD+B3H21nS5775zSnsJyrn19JZkEZf7slrTHYA3zzzMGEuhy88MW+Hvs7tMVWPXzw3SYoqzPdszRfvm2q11rvwrJq/rpsH1vyitscGGqP99fncbyylltnDG775A5KHdiH+KhgFm4+xOWpLVe2eLM5t5iJSVEnpQNEhBFxEez0QRnfuv3uVMLkQX3aONOtf2QwP5kzmqc/283cP69geko0d81K4dwR/b0GiZ5ypKSSXy/cTqBDWDjgbFK64dvHqyuzCHQIN05v/zfG1EF9eeCiEWQVlDFzWAxnDY9hQLMOSKjLyVt3Tefml9Zw12sZPH1daru+QVjt/XW5GANXtlCtJSI8ftUEZj+9nPveXM8fr5nIt/+RQWVNPf/41rRTxjT6hLq47oxBvPZVFj/42kgSvVQ09TRb9fDBXYtf7oO1PtZkFhIbEURyv1Cvr0eHuUiICm5cMrgrjDG89lUW4xIjvS4V0FUBAcIl4+L4Ylc+pR3Y87WsqpY9+aUn5e8bjIyLYOeh45YtXX28sqZdg8AZ2UUMiAzq0A/jt85OYeXD5/PInNFkHy3n9lfS+dpTy3gnPYeqWt+MD/1rXR519YbAgAD+552N1FpcN368soZ303O4bEIC/SM69o3xexcM54lrJ3HllKRTgn2DvmEu/nnnNCYN7MN9b67jXxk9u1idMYb5GblMT4lmYLT3n1Fwt/Op6yaRfbSMK/6yEoB37zmzxQHsO84egsH97as3sCTgi8glIrJTRPaIyENeXg8Skbc9r68WkWQrrtsZIS4H5T28MbUxhtX7Cpk2JLrVga6xiVGWpHS+2neUXYdLufnM1gfWumLO+Hiqa+tZsuNIu//M1gMlGIPXaphRcREUV9RwuKTrA9e1dfVc/fxXXPLkMgrbmBWc4VkwraP3KSI4kDtnpbDsR+fx5LUTcQQIP5q/ibN/v5Rnl+7hSA/ukmWM4d30HM5I7stvrxzPxpxj/OVzawcL303Ppay6jltbKMW0QmRwIK/dMZUZQ2P4wbsbeX1Vdrddq7mM7CKyjpZz1ZS2x3Kmp/TjodmjmDiwD/PvmcGIVmrtE/uEMHdiAm+u2U9xuW+q0JrqcsAXEQfwLDAbGANcLyLNF2O5AygyxgwDngR+39XrdlaYy9njOfzcogoOlVQybUjrA5JjEyLJLCijrIsfSK+tzKZvaGC3ThCaMqgv/SOCOlSt05DzHpfopYfv+aHZYcEErLfW5rDj0HEOllTywDsbWlzl8khJJblFFV36FhToCODy1CQ+uv9sXrt9KiPjInh80U6m/3YxN7+0hvfX53Z7kUB6dhH7Csq4Jm0gl01IYO7EBJ5ZvNuyXajq6g2vfpXF5EF9mDiwfamvzgp1OfnbLWlcOLo/P/33Fl5Y1jNVLvMzcgl1uZfQaI+7Zg3lg+/ObPXbQIO7z0mhvLqO11dldbGVXWdFD38qsMcYs88YUw28Bcxrds484FXP4/nABeKj2QghLkePV+k0rLI4dUi/Vs8blxCFMbD9YOeDXt6xCj7Z5p4J29ZEqq4ICHBX6yzdeaTd93NTbjHxUcFeUwIjLVpTp6Syhic/3cXUIdH8cu5YPt+Zz/MtBI3G/H07B2xbIyLMGhHL63dM47MHzuE75w5j75FS/uftjaT932c88PYGlu/O75aa9LfX5hDmcjTmvX81bxwx4UF8/+31lixV/MGGPLKPlnPn2Sldfq/2CA508NxNU7hsQjy/WbiDpz/b3a3Xq6iu48NN7tr7sCDrhzVHxUVy7shYXlmZ5fOlo60I+IlA00LbXM8xr+cYY2qBYuCU6Ccid4lIuoik5+fnW9C0U4UF9XyVzprMQvqGBjK8f+sDaWMT3aVbXcnj/8PzNfimDgysddbs8fFU1tSzdEf7/q0alkT2pk+oiwGRQV0O+M8u2UNheTU/vXQM35w+mMsmxPOHRTtZ7WVp44zsIlzOAMYmWFsyN6x/OA9+bSTLf3Qeb981nbkTE/h0+2G++fc1nPnbxfx5yW7LcuzHK2v476aDfH1iQuM8gqjQQB6/egJ788t47OOdXXr/mrp6nvpsN2PiI/na2Pb1fq0Q6Ajg6etSuXJyEk9+tqtbc/reau+tdvesoRSUVvOvdb7dSMeKgO+tp968G9OeczDGvGCMSTPGpMXGds907JDAnk/prMkq5Izk6DarOOIig+kX5mos+eqoypo63lqzn4vGDCCpb9tfNbvqjORoYsJdfLCh7YlIxRU1ZBaUtZoSGBkX2aVKneyjZby0IpMrJycx3lMJ9LsrJ5DcL4z73lx/ypK9GdlFTEiMaleJYWcEBAjTUvrxuysnsPaRC/nLjZMZmxDJHz7ZxTV//cqSVRg/3HSQipo6rmk2j+Ds4bHccuZgXlqRyco9BZ1+//kZuewvLOcHF4/o8SokR4DwuyvHM2NoPx5+b3PjNzKrzc/IZWB0CFO7cQ7I9JRoJg7sw4vL9vl05rEVAT8XaPq/LQloPve88RwRcQJRgE/mHLt7+D2X0jlUXEn20XKmtpG/B3daYGxiVKd7+P/ZeICi8hpuOTO5U3++oxwBwrVnDOTT7Yfb7Jlv9XyItdTDB/fA7e4jpZ3u/f524Q4CHQH88GsjG4+FBzl59kb3LMnvv7Wh8YetqraOLXkllqRz2iM40MGc8fG8fNtUnrk+ld2HS5nzzHI+7OKWgO+k5zC8fzipXj5IH5o9mpSYMB58dyPFFR0fMKysqeOZxbtJHdSH80f171I7OyvQEcCzN0wmLiqYu1/P4GBxhaXvf6Ch9j41qVs/0ESEe2alkHW0nEVbW58rUVtXz+FuGvS3IuCvBYaLyBARcQHXAQuanbMAuMXz+CpgibGq/q6DQlyOHt3isKH+fnpK6/n7BmMTItl1+HiHy/uMcQ+sDe8fzplD23ctK9x5dgphLidPL259/fNN7Qj4IwdEUF1bT9bRjvd8V+07ysdbD3HPOUNPKf0bHR/Jo/PG8uWeAv60xJ0P3pJXQnVdfbeUrbZl7sQEFt5/NsP6h3PvG+v58fxNneqE7D58nPX73bOEvQ2JhbgcPHHtJA4fr+KXC7Z2+P3fXLOfg8WVPHjxSJ8uANY3zMXfbkmjvKqWu17LaHcePCO7kF/+Zyuf7zzSYq/6/fV5rdbeW+nisXEk9wvlr1/s9Vp+vP9oOX9YtJOzfr+U+95Y3y1t6HLA9+Tk7wUWAduBd4wxW0XkURGZ6znt70A/EdkDPACcUrrZU8JcTqpr63usl78ms5DwIGfj2tptGZcQRW29Yffhju0AtW7/MbbklXDzjO4rxfSmT6iL22cms3DzoVYHmzfnFjMwOoS+nn1yvenswG1dveFXH24jPiq4xYHFa9IGcsXkRJ5evJsVewpYl90wYNu9VSctGRgdyjt3n8l3zxvKOxk5XPanL9nawZLct9fm4AwQLk9tPmR2wqSBffjuecN4b31ehwq9OPsAABL/SURBVCqqyqtreXbpXqanRDOjBzsQLRkxIIKnr0tly4FifjR/U6vzNWrr6nni011c/fxXvLIyi1tfXsusx5by9Ge7OXDsxDeEhtr7aUOiGdTC/BgrOQKEO2elsDG3mFX73AmOypo6PtiQxw0vrmLW40v5y+d7GB0fwe1nDbFsTkpTltThG2MWGmNGGGOGGmN+7Tn2M2PMAs/jSmPM1caYYcaYqcYYn801biiN/GBDz6x4uDqzkLTkvjja+XWxYQCxo3n8V1dmERHk5IpWfvi7yx1npRAR7OSpz1ru5W/MPcaExNaD67D+4QQIHV4b/1/rctl6oISHZo9q3NWsORHh/74xjmGx4dz/1no+3XaYQdGhHZ5EZCV3+mkU/7xjGmVVtVz+7EpeXpHZrh/06tp63lufx4WjB9CvjaWa7zt/GBOSovjJ+5vJLWrft6fXvsqmoLTK5737pi4cM4AHLx7Jgo0HeK6FRcmyj5Zx1fNf8czi3XwjNZGM/72IZ2+YTEpsGE9+touzfr+E215ew8dbDrE6s5DMgrJuHaxt7srJScSEu3jy0138YsFWpv1mMfe/tcE9TnLRCFY8dD4v3zaVS8bFdct9t91M26lDohkdH8mrK7O65RO0qYLSKvYcKWVaG+WYTQ2KDiUiyNmhCVj5x6tYuPkgV6UldUtZWVuiQgO546whLNp62OsHVWFZNblFFW0uPxwc6CA5JqxDu1+VVdXy+KKdTBrYp815B6EuJ3+5cTJlVXWsySps93IK3W3GsBg+un8Ws0bE8Mv/bONnH2xt8//mkh2HKSyrbteib4GOAJ64ZhK19YYbXlx9Ui/Xm+OVNTz/xV7OHRnb44vZteU75w7l6xMTeHzRTj7bdmLdnYbJZ3OeXs6+/FL+dH0qT1wziegwF5dOiOf1O6ax/Efn8d3zhrHtYAn3/CODG15cRajLPbbSU4IDHdw2cwhrsgp5Y/V+Zo2I5Z/fmsayH57HfRcMJz6qe5dfsF3AFxFunTGYHYeON36t6i7pWe73b8+AbYOAAGF0QmSHBm4/3XaY2nrT7hUfu8PtZw0hMtjJU15qpjc35O/bCPjgHrjtyNZ4z3+xl/zjVfz0sjHt6hENHxDBb64YB7Q9L6InRYe5ePHmNO6alcLrq7L54yetj4m8vTaHuMjgdm8uMqx/OK/fMY2ismquf3FVq4Off/8yk2PlNfzgopEtnuMrIsJjV05gXEIU97+1nl2Hj3OsvJp731jPD+dvYlxiFB9/fxZf9/LhPzA6lB9cPJIVPz6fv9+SxsVj4rjv/OE93kn61tlD+MuNk1n9kwv40/WpzBwW02MVULYL+ADzJiXSJzSQV1dmdet1Vu0rJDgwoNWBSm/GJUSx3bNufHss2XGExD4hjbNVfSEyOJA7z07hs+2HT1lFcnMrM2ybGzkgkuzC8naNseQdq+CFZfv4+sSEVjfjaO7y1CQW3DuzR7/Kt4eI8PDsUVw/dSB/XrqHF5d5z3weKq7ki135XDUlqd2pQnDn81+7YypHS6u54cXVHCo+tRKkqKyavy/P5GtjB7TrA9oXQlwOXrh5CiEuJ7e/spZLnlrOoq2H+PElo3jjzulet11syukI4ILRA3j+m1P49rlDe6jVJwQ53d8qWhvP6i62DPjBgQ6unzqIT7YdandOszPWZBYyZXDfDm8+MjYhksqaevbltz1wW1lTx4o9BZw3KtbnudZbZybTJzSQJz89uXe6KbeYlJiwdq2dPzIuAmNo16D17z/aAcCPL+l4T3RCUh/LNoWxknusYTyXjo/n1wu38/ba/aecMz8jh3oDV6d1/AMrdVBfXr19KkdKKrnhxVWnrPnzwvJ9lFbX8kAv7N03FR8Vwl+/OYUjJVWEuhy8/52ZfPvcoR36ALSj3vc/vofcNN29bHB3LdBUXFHD9kMlTE3ueNqgoSfcnjz+6sxCKmrqfFYn3VREcCB3zUph6c581jeZJLM5r7jdvcVR7azUycguZMHGA9x5dkqPTDLrSY4A4clrJzFrRCwPv7eZhU2qa+rrDe+ku1d1HNyvfdtSNjdlsDvoHyqp5LoXV3HkuDvo5x+v4pUVWcydmNBYMdWbTRncl89/eC4L7z+7134b6W1sG/AT+4TwtbFxvL02p92bmlfW1PGfjQeorm17YlB6ViHGdCx/32BobBhBzgC25rWdx1+64whBzgDOTPHtTkENbjkzmegwF096cvlHjldysLiy3WmtgdGhBAcGtDpwW1NXz0/e20J8VDD3+OAreU9wOQN4/qbJpA7qy/1vrWfZLvfyFaszC9lfWN7l8Zq05GheuW0qh4orueHF1eQfr+K5z/dSXVfP/RcMt+Kv0CMS+oR065pR/sa2AR/glhnJHCuvadfSAAC/WLCV+95cz3PtWHp2TWYhLkcAqZ2oBHE6AhgVH9lmD98Yw5IdR5g5LKbFcsSeFhbk5O5ZKSzblU9GdmHjio3tXWXRESCMGND6wO0Ly/ax8/BxHp03jnAfVCX1lFCXk5duOYOhseHc/XoGGdlFvJOeQ0Sws3FT+q6YOiSal249g7yiCq574Sv+sTqbKycndsvmKap3sHXAnzYkmlFxEbzSjhLNDzbk8dbaHKLDXDz3xR7y2ihtW51ZyMSBUZ3ufYz1VOq01q69+WXsLyznvF6Qzmnqm2cO9tQa72ZTbjEBAmPaOfEM3DNuW+rhZxaU8fTi3cweF8dFYwZY1eReKyo0kNfvmMaAyCBue3kNCzcfZN6kBMt6tdNT+rmD/rEKjDHcd/7p07tXHWfrgO8u0Uxmx6HjrM5suUQzq6CMn7y3mSmD+/L+d2ZgDPx24fYWzy+rqmVzXnGn0jkNxiVEcbyylpzClj9Ylno2H+kN+fumQl1O7jlnKF/uKeDd9ByG9Q/vUOnbyLgICkqrONpssTNjDI+8v5kgRwC/mDvW6mb3WrERQbx+xzRCXU6qauu5Ns3alVDPHNqPd++ewQs3p7VrfXd1+rJ1wIcTJZqvrMjy+npVbR33vrkOpyOAZ65PZXC/MO45ZygfbjrodcldcK+zXldvOjThqrlxjUslt5zWWbzjMCMHRPSKvTKbu3HaYGIjgjhQXMn4NmbYNjcqzv13bz5w+691eazce5Qfzx7V4lZ5/mpgdChv3z2dJ66Z2Ph/w0rjk6I4b2Tv6jgo69k+4Ie4HFx3hrtE01ua5ncf7WBLXgmPXTWhMbDec85QEqKC+eV/tnmtlV+TWYgjQLq0EuOIARE4AqTFPH5JZQ3pWUW9Lp3TIMTl4NvnuAdU25ph21xDhUjTtM7R0ip+/d9tTBnclxumdv9a/73R4H5hXDE5yeflt+r0ZfuADyc2C3n9q5NLND/ddpiXV2Rx64zkkzZ/CHE5+Mmlo9l2sIS31+bQ3Op9hYxLiOzSgGJwoIPh/cNbnHG7fFcBtfWm16Vzmrpx+iAeuGhEh7dajAl3ER3mOqmH/+v/bqe0qpbfXjG+x9dlV8pfaMAHkvqGcvGYON5au79x6dUDxyr44fyNjEuM5OE5o075M5eOj2fqkGj+8MnOkzYnrqypY0POMaa1cznk1oxNiGJLC6WZS3YcISoksNesB+NNkNPB9y4Y3uEZhSLCyAERjZuhLN+dz3vr87jnnKGtbhitlGqdBnyPpiWatXX1fO/N9dTU1vOn6yd73RFJRPj518dwrLyap5qsBb8x5xjVdfWW7J4zLjGSgtKqU2ZD1tcbvth1hFkjYnE6/POfcKRnTZ3y6loeeX8LQ2LC+O55w3zdLKVOa/4ZLTpheoq7RPPlFVk89dlu0rOL+M0V4xkS0/JsxrEJUVw3dRCvfZXNbk9vdE1mISLu7f+6amyC9xm3m/KKKSit5vxR3bMNZG8wKi6C8uo6fjR/E/sLy/nN5eN1go1SXaQB30NEuMVTovnnpXu4Nm0g8ya1vbb8gxePJMzl4NEPt2GMYXVmIaPiIokKbXvdmLaM8ayN33zG7ZIdRwgQOGdE783fd1XDwO2Hmw5yTVpSj+7ipZS/0oDfxDcmJdI3NJDh/cPbXecdHebify4awfLdBXy05RAZ2UWNm6x0VXiQkyExYaf08JfuOELqoL5E+2C1vZ4y3JOr7xfm4idzRvu4NUr5B/+dl94JIS4HC+49i8iQwA4tVXDT9MG8sXo/P5q/iYqaui5NuGpubEIk6/efWG74SEklm/OKT9qo2x+FBzn53vnDOGNINH1C/feDTamepD38ZgZGhxIV0rF0TKAjgJ9/fSylVe413K0N+FHkHavgWHk1AJ/vdC+iZYdJMg9cPJKzh/vvOIVSPU0DvkXOGh7DpRPimZgURUwbe4x2xIkZt+48/pIdR4iPCmZ0vJYnKqU6RlM6FnrmulTqLd4nt6FSZ+uBYtKS+7J8dz5zJyXqbEulVIdpwLeQI0BwYG0gjg5zkRAVzJa8EtZmFlFW3Ts2O1FKnX404J8GxiREsfVAMUt2BOFyBjBzmJYoKqU6TgP+aWBcYiSLdxymsuYQ01P6EerSfzalVMd1adBWRKJF5FMR2e35/ZTlIUVkkoh8JSJbRWSTiFzblWva0biEKIyBvGMVXKDpHKVUJ3W1SuchYLExZjiw2PO8uXLgZmPMWOAS4CkR6b0rfvVCY5usf675e6VUZ3U14M8DXvU8fhX4RvMTjDG7jDG7PY8PAEcALa7ugLjIYPqFuRjWP1x3JFJKdVpXk8EDjDEHAYwxB0Wk1e6niEwFXIDXXcBF5C7gLoBBg+y5yYU3IsLDc0bT14L1eZRS9tVmwBeRz4A4Ly890pELiUg88DpwizGm3ts5xpgXgBcA0tLSrC1oP81dNSXJ101QSp3m2gz4xpgLW3pNRA6LSLyndx+PO13j7bxI4L/A/xpjVnW6tUoppTqtqzn8BcAtnse3AB80P0FEXMD7wGvGmHe7eD2llFKd1NWA/zvgIhHZDVzkeY6IpInI3zznXAPMAm4VkQ2eX5O6eF2llFIdJMbitV+skpaWZtLT033dDKWUOq2ISIYxJs3ba7paplJK2YQGfKWUsgkN+EopZRMa8JVSyiZ67aCtiOQD2V14ixigwKLmWEnb1THaro7RdnWMP7ZrsDHG6/I1vTbgd5WIpLc0Uu1L2q6O0XZ1jLarY+zWLk3pKKWUTWjAV0opm/DngP+CrxvQAm1Xx2i7Okbb1TG2apff5vCVUkqdzJ97+EoppZrQgK+UUjbhdwFfRC4RkZ0iskdEvO2x6xMikiUimz2rhfp0VTgReUlEjojIlibH2tyQ3kft+oWI5DVZaXVOD7dpoIgsFZHtIrJVRO73HPfp/WqlXb6+X8EiskZENnra9UvP8SEistpzv972LJveG9r1iohk+nolXxFxiMh6EfnQ87x77pcxxm9+AQ7c2yem4N5KcSMwxtft8rQtC4jxdTs8bZkFTAa2NDn2GPCQ5/FDwO97Sbt+ATzow3sVD0z2PI4AdgFjfH2/WmmXr++XAOGex4HAamA68A5wnef488C3e0m7XgGu8tX9atK+B4A3gA89z7vlfvlbD38qsMcYs88YUw28hXujddWEMWYZUNjscJsb0ne3FtrlU8aYg8aYdZ7Hx4HtQCI+vl+ttMunjFup52mg55cBzgfme4774n611C6fE5Ek4FLgb57nQjfdL38L+IlATpPnufSCHwIPA3wiIhmezdp7m5M2pAda3ZC+h90rIps8KZ8eTzU1EJFkIBV377DX3K9m7QIf3y9PemID7i1PP8X9rfuYMabWc4pPfi6bt8sY03C/fu25X0+KSFBPtwt4CvgR0LDXdz+66X75W8AXL8d6xac4MNMYMxmYDXxXRGb5ukGnieeAocAk4CDwR180QkTCgX8B3zfGlPiiDd54aZfP75cxps4YMwlIwv2te7S303q2Vae2S0TGAQ8Do4AzgGjgxz3ZJhG5DDhijMloetjLqZbcL38L+LnAwCbPk4ADPmrLSYwxBzy/H8G9x+9U37boFIc9G9HT2ob0Pc0Yc9jzg1oPvIgP7puIBOIOqv80xrznOezz++WtXb3hfjUwxhwDPsedK+8jIk7PSz79uWzSrks8qTFjjKkCXqbn79dMYK6IZOFOQZ+Pu8ffLffL3wL+WmC4Z4TbBVyHe6N1nxKRMBGJaHgMXAxsaf1P9bg2N6T3hYag6nE5PXzfPPnUvwPbjTFPNHnJp/erpXb1gvsVKyJ9PI9DgAtxjy8sBa7ynOaL++WtXTuafGgL7jx5j94vY8zDxpgkY0wy7ni1xBhzI911v3w9Om31L2AO7oqFvcAjvm6Pp00puCuGNgJbfd0u4E3cX/drcH8rugN33nAxsNvze3QvadfrwGZgE+4gG9/DbToL99fpTcAGz685vr5frbTL1/drArDec/0twM88x1OANcAe4F0gqJe0a4nnfm0B/oGnkscXv4BzOVGl0y33S5dWUEopm/C3lI5SSqkWaMBXSimb0ICvlFI2oQFfKaVsQgO+UkrZhAZ8pZSyCQ34SillE/8P08HUNnra0pAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute autocorrelation values, which are the correlation of x with itself, lagged\n",
    "plt.plot(ts.acf(random_values))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above graph, we see the values correlate exactly with itself with no lag - unsurprising!\n",
    "\n",
    "However, after this, any other lag value has a near-zero correlation, indicating no correlation between the values and the lagged version.\n",
    "\n",
    "Let's now create a time series with dependency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here is an example where value (n) is dependent on value (n-1)\n",
    "values = [0]\n",
    "\n",
    "for i in range(100):\n",
    "    # Add a random value to the previous value. While the values are random, they are random, but biased\n",
    "    values.append(np.random.random() - 0.5 + values[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c8b7da1708>]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\marin\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\stattools.py:541: FutureWarning: fft=True will become the default in a future version of statsmodels. To suppress this warning, explicitly set fft=False.\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c8b623fcc8>]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts.acf(values, nlags=100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, the values are correlated with itself (as per the definition of correlation), but the correlation stays high as the lag increases. This shows that the values are dependent on themselves.\n",
    "\n",
    "If your data is autocorrelated, you should remove this before computing cross correlation with other time series. You can remove autocorrelation with a process known as pre-whitening, which removes the autocorrelation.\n",
    "\n",
    "An example of a method for this is Holt Winters. Techniques like this are also known as smoothing algorithms, but that term has multiple meanings, and smoothing algorithms have multiple uses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.tsa.holtwinters import SimpleExpSmoothing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = SimpleExpSmoothing(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_fit = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c8b7fab948>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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E771S5HGTlwlxsbwiyAEe2pzFx5YnsiLVeSG1ZWE8MROMbJmK5UPDIw9Utth9rIv1XkkjrxXU8dCmLMwhYxfrcKXoYD/WZ0XzyuHaMePvewcGKahuo7PPwvG6DhdVKIRreU2QZ5qD+eltS91iRZ/06CAiAn04UDEzQd5nGeS7LxeSFhXIZzdmzMg5p+qGJQlUNndzuGr0lAtHq9sYGLSFe36FZy+/J8REvCbI3YlSiuUpETPWIv/9++WUn+niuzfm4GeanT/ors6Jw9do4OVDo7tX8k7Z/oxC/U3kzdAPPiFmGwnyWWp5agQnG7to7e536nmqW3v437dPsCUnjsvOmxBsNgkL8GHjXDOvFdSOugmcX9FCRnQQG+ZEj4S6EN5GgnyWWjbUT37wtHPnHXnpYDW9A1a+cd0Cp57HEa5bHEdtW+/In4nWmgOVLSxPjWBFaiTVrT3UtfW6uEohZp4E+Sy1JCkcg4KDTu4u+PDkGebHhZAcGejU8zjC5Qti8TUaeO1oLWBbyai5q5/c1Ahyh25i50k/ufBCEuSzVJCfiflxoRyoHL9F3m+x0tU38WpGF6N3YJC8Uy2sy4y26zgzJdTfh0vmRPNaQR1aa/KHfsitSI0gOyGUAB+jdK8IryRBPoutSI3g0OnWccdH//DVYm7+9W67jn+gooU+i5X1WVF2HWcmXbMonurWHg5XtZFf0UJYgA+Z5mB8jAaWJIeNhLsQ3kSCfBZbnhpOZ5+FEw1jx0fvK2+mpL6T+vbp9wnvPnkGo0GxKj3SnjJn1JULYvExKl49Wkt+RQvLU8IxDD1AlJsaSVFtu92/qQjhbiTIZ7HhJywPVIzuXum3WEfC3Z6x5rtLm1iSFDbyKLw7CAv0YX1WNC8erOZEQ+eoB7xWpEUwaLUtri2EN5Egn8VSIgOJCvIdM578REPHOQ/BTBzku0oa+fJfD427GlF77wBHqlpZn+Ue/ePnunZRPI0dfQCsSD3728TylAiUQsaTC68jQT6LKaVYnhpB3qnRIzGGV/GJCfEjf4KHhvotVr75UgEvHKzmeP3Yrpm9Zc1YNW5zo/NcV2XHYjIojAbFkuSwke1hAT7MjQmRIBdeR4J8lludHsmppm4azukLL6ptJ8DHyNalCRRWt4+7wPNf805T2dwN2LpQzre79IxtgqxU50wi5kzhgb5snh9DbmoEgb6jF7lalxXFnpNNo9ZpFcLT2RXkSqlblVKFSimrUirXUUWJs1an20aU7Ck/2yovqmlnfnwIuWmR9A9aKawZPf9IT/8g/7vzBCvTIkiNCuSjk2fGHPfDk2dYmRY5ax/Jn8wv71jGHz6zasz2e9ano9E8+k6pC6oSwjXsbZEXAB8DdjmgFjGOBfEhBPuZ2Fdua1VrrSmqbSc7PnTCm6F/+PAUDR19fGXLfNZlRrO3rHnUIs8NHb2U1He6ZbfKMH8fIwG+Y38IJUcGcltuMn/df5qqlm4XVCbEzLMryLXWxVrr444qRoxlMhrITYtgb5mtRV7V0kNHr4XshFDMIX6kRAaOuuHZ1j3Ab94tZfP8GFamRbI+K4qOPgtHq8+22t8vsbXQ3Wn8+FR8flMWCiWtcuE1ZqyPXCl1v1IqTymV19jYOFOn9Qir0iM50dBJU2ffyCr3w8uxrUiNIL+yZWRkyi92nqC918K/XzUPgLUZtrD+8OTZFv2f9lSQFhXIwoSw80/lERLCA7hjVTLP5VVR2SStcuH5Jg1ypdQOpVTBOF9bp3IirfXjWutcrXWu2WyefsVeaLiffP+pZopq2jEomB9nC/LlKeE0dvRR1dLDRyeb+L8Py/nUmpSR5dqigv2YHxfC7lJbK/xAZQuHT7dy74b0kQdpPNGDm7IwGBS/fPuEq0sRwulMk+2gtb5iJgoRE1uUGIa/j4E9Zc1Ut/aQYQ4e6R9ePvRAzHsljfzm3ZOkRQXx9WtHz2S4Piuap/ZU0DswyO/fLycswIdbViSNOY8niQ3159YVSTyXX8UPb16Er0kGaAnPJX+73YCvycCK1Aj2ldta5Oeucj8vNoQgXyOPbCuitq2Hn9y2ZMyQvPVZUfRbrPzjUDVvFNZx5+qUMft4orWZts890aLNQngKe4cf3qyUqgLWAtuVUm84pixxvlVpURTXtVPd2jNqlXuT0cCS5HD6LFY+vylr3IWTV6ZFYjQovvdKEUaD4u51aTNYuesML7R9SB7ZFx7O3lErL2qtk7TWflrrWK311Y4qTIy2OiOS4Sftz22RA9yam8SWnDi+sHnOuN8b4u/DkqQwuvoHuWFxArEOWCDaHSSGBxAd7MehCaYCFsJTSNeKm1iaHI6v0Xa5FpwX5DcvS+Kxu1ZcsB94wxzbDeZ7NqQ7r8hZRinF0uRwDlVJkAvP5vkdpR7C38fI0uRwTjV1YQ7xm/L3f/aSdNZkRLIw0TOHHE5kaXIYO4rraeseICzQfWZ5FGIqJMjdyLdvyKatZ2Ba3xvi7+PWT3JO19Jk2z2Dw1WtbJwrw16FZ5KuFTeyMDHMLaeddaXFyWEohcxRLjyaBLnwaKH+tqXgZOSK8GQS5MLjLUkK59Dp1nEX2BDCE0iQC4+3NCWcpq5+qlpkjnLhmSTIhcdb5qUPBnX3W2jt7nd1GWIGSJALjzcvLgQ/k8HrgvxbLxVy++N7XF2GmAES5MLj+RgNLEwM87qRK3kVzRyr66CurXfynYVbkyAXXmFZcjhHq9vot1gn39kDtPcOUDE0F/ve8rFrtgrPIkEuvEJuWgR9FuuolZI8WVHN2Rkf95Q1X2BP4QkkyIVXWJkWCcC+cu8ItcKhIF+cFMbeMmmRezoJcuEVooL9yDQHsf+UtwR5G+YQP65fHE/ZmS4a2s/2k/9t/2keeCoPq1XG1XsKCXLhNValR5J3qnnWB9hDfz7A3/aftusYRTXt5CSEjiwTuGfoN5F+i5Ufv3mcNwrr2Xa01q5zaK0pqe+QB61mAQly4TVWpkXS3mvheH2Hq0uZUEN7L9uO1PLbXSenHZC9A4OcaOgkJyGUnIRQgv1MI90rrx6tpaGjj1B/Ez/fUYJlcPo3f98qqueqn+3ioT8fpLPPMu3jCPtJkAuv4Q795PuGun5ONnZN+wdOSX0Hg1ZNTkIYJqOB3LQI9pY3o7XmiQ/KyTQH8V+3LKassYuXD9dMu9aPypowGRSvF9Zx468+oGQW/4D0dBLkwmskRQSQEOY/Epaz0f7yZvx9DBgUbDs8va6P4RudOUNLAq7JiKK0oZPXC+o4Wt3GZ9ansyUnjuz4UH6x8wQD02yVH6hsZXlKBM/ct5r2Hgtbf7WbExLmLiFBLryGUoqV6ZHsH2qdzkb7TrWQmxrJ2swoth+tnVadhTVthPiZSI4IBGB1uu03kW+8VEBYgA8fW56IwaD48pVzqWjq5oUDVWOOMdmi1b0DgxTVtLEsNZw1GVFs+8IGDAp+sfPElOsV9pMgF15lZVokDR19VDZ3u7qUMdp6BjhW187KtEiuX5xA+Zmukdb1VBTWtLMgIRSDQQG2eeyDfI00d/Vzx6oUAn1t68lcviCGJcnh/HJnKYPn3QD+9bulXPfLD6hvH/+p0ILqNgYG9chi33Fh/ty9Lo3tR2spbZBW+UyTIBdeZdVQ63TvLOwnP1DRgtawMj2Cq3PiMBoU26c4smTQqjlW2zHSrQK2KQpWpEViNCjuXpc6sl0pxQMbM6hu7eH9E40j27XW/P1AFYNWze7SM+PXWtkCMBLkAPduSMffZORXb5dOqWZhPwly4VWyzMGEB/qwv7yZ3oFBXjtayxMflM+KIYl7y5vxMSqWJUcQGeTL+qxoth2pmVL3SvmZTnoGBslJGL0261eunsfPP7GU+LCAUdsvXxBDeKAPz+ef7V7Jr2jhdLNtyt8PJgjyg5WtJEcGjFo/NirYj7vWpvLy4RrKz3RddM3CfhLkwqsYDIqVaZG8VlBH7vd38M/PHOCRbUU8l2/fuG1H2H+qmYWJYQT4GgG4flE8p5t7pjStwPk3OoctTAzjhiUJY/b3Mxm5aWkibxbZFqgGeOFgNQE+RjbNM7O79MyYHyRaaw5UtoxqjQ/77CUZ+BgNPPqOtMpnkgS58DrXLYrH38fItYvieOreVaxKj+QH24tp7OhzWU29A4McqWpl1dAQSYCrc+LwMSpuf3wPOd9+ncyvv8oPXy2+4HEKqtvwNRnIigm+6HN/fEUS/RYrLx+ups8yyPYjtVyVE8tVOXHUt/dxsrFz1P41bb3Ut/eNG+TmED8+uTqFFw9Wc3oK9yHeLKyjpUvmTp8uCXLhdW5alkjeN6/gvz++hEvmmPnhzYvoHbDyyLYil9V06HQrA4N6ZKw7QFigD/9540JuWpbI7atSyI4P5fn8qjE3Js91uKqNBXEh+Bgv/p92TkIo8+NCeD6/inePN9LWM8DNyxLZMLTQ9wcnRnevHKgY2z9+rvsuyWDQqnnpYPVFnf9kYyf3P5XPr9+VVvx02RXkSqn/UUodU0odUUq9qJQKd1RhQsyUrJhgHtyUycuHa3jneINLatg/dPM1N210OH5ydQo/vHkR37o+m89uzKC5q59Dp1vGPUZP/yAHK1tYkxE1pXMrpbg1N5nDVW38fMcJooN92ZAVTXJkICmRgXxQOnrSrQOVLfj7GJgfHzLu8RLDA8hNjbjoG7VvFNYB8PYx1/zZewJ7W+RvAQu11ouBEuBr9pckxMz758syyTQH8c0XC+izDM74+fedamZebAjhgb4T7nPpXDMmg+KtovEDb/+pZgYGNWszpxbkADctTcBkUBTXtnPDkgRMQy369VnR7ClrGvUo/4HKVhYnhV+w1X/94niO1XVc1FDENwvrAdvTrJVNs29YqDuwK8i11m9qrYcnWdgDJNlfkhAzz89k5Ktb5lPd2jPj83e39w6QX9HCyvTxuyqGhQX4sCo9kp3F9eO+/+FJ2yPzw0MspyIq2I/LF8QA8LFlZ/8Zb8iKprPPwuEq2w3X4QeBJupWGXbNoniUgm1HLtwqr2vr5dDpVm7LtZ3z7WPjfzZxYY7sI78HeG2iN5VS9yul8pRSeY2NjRPtJoTLbJxrxt/HwNsTBKWzPPVRBd39g3wiN2XSfS9fEMuJhs5xW64fnjzDspTwkQd+purfr5rHV7bMY2Hi2REvazOjUIqR8eTvlTQOPQh04V7U2FB/VqVFsu3IhZ9OfavI1q1y/8YMMqKD2CndK9MyaZArpXYopQrG+dp6zj7fACzAMxMdR2v9uNY6V2udazabHVO9EA7k72NkQ1Y0O481zNgj/D39gzz5QTmXzjWzKCls0v2vGGo17zjvh01b9wAF1W2sy4yedi1zYkN48LIslFIj2yKDfMlJCOWtonr+47nDPPBUPvFh/qy+iH746xfHU9rQSUm9bdRLfkUL6//rbbYdOTtR1xuF9WSYg8iKCWHz/Bj2ljXTJTMpTtmkQa61vkJrvXCcr38AKKXuBq4H7tSzdQILIS7S5vmxVLX0cKKhc/KdHeAv+ytp6urn85uyLmr/1KggsmKC2XleF8Se8iasGtZNo398Muuzojla3cZLh6p54NIM3vzXjYQF+Ez6fVsWxtsm/zpSQ3FtO5/5v31Ut/bw1eePUNHURVv3AHvKmrgqOw6AzfNj6B+0Tvg0qZiYvaNWtgBfBW7UWstdCuH2Ns+3tXh3Fjv/V/x+i5XHd5WxKi1ySv3aly+wtVzbewdGtn10sgl/HwPLJum7no671qTymfVpvPmvl/K1axYQ4j95iINtTPmajCheOFDNXU/sI9DXxF/vX4PRoPjiswd5o6gOi1VzdU4sALlpkQT7mVw2csid2dtH/isgBHhLKXVIKfWYA2oSwmXiwvzJSQidkZtuLx6soratlwc3ZU7p+65YEIvFqtlVcvZe0+7SM6xMi8TX5PhHQ5IiAvnODTmkRwdN+XuvX5xAdWsPg1YrT9+3itUZUfzolsUcrmrjuy8XEhPix5IkW3+7r8nAxrnRvD1B11ZVSzfd/dLtMh57R61kaa2TtdZLh74+56jChHCVy+fHkF/R4tQnDbv6LPz63ZMsSgzj0rlTu2e0PCWCiEAf/vjhKdp6Bmjo6OVEQyfrs6bfP+4s1y+J55blSfzpntVkxdjGnV+zKIZap0YAABGsSURBVJ5Prk6hu3+Qq3JiR2ZpBNg0L4b69r4xsz6+XlDH5h+/xx2/20vvwMwPD53t5MlOIc6zeUEsVm0boeEMlkErD/35AKebu3n4mvmjbi5eDKNB8fA18zlY2cp1v3yf379fDjinf9xeof4+/OS2JWNu5H7rumz+aW0qn16XPmr7ZfNiMCj46t+PsGdoebrn8k7z4DP5JEUGcPh0K998qWDWzifvKhLkQpxncWIY0cG+TnnSUGvNt/5RyDvHG3nkpoXTbkV/YmUKf/vcWrSGx3eVEepvGjPj4WwW4Gvke1sXjpkTxhzix//esZzmrn5uf3wPH/v1bv7j+SOsy4zmlYc28MXL5/B8fhV/+PCUawqfpaY34FQID2YwKDbNi+GNwjoGBq1TmrfkfEU17Tz8whH8TUZyEkPpt1h5dl8lD16WyZ2rUyc/wAUsT4lg+xc38L1XikiODMRomFrLfra6bnE8ly+I4cnd5fzmnZNcuyiOn31iKX4mI1+6fA7Fte18f3sxc2NDZmV3kisoV/yKkpubq/Py8mb8vEJcrHeONfCZP+znuzdk8+n16ZN/wzg+OtnE/X/KI9DPSGJ4AEW17fQOWLl5WSI/vW3JlLtUvNHAoBWTQY36s+roHeCW33xIdUsPz3x2DUuTvWeKJ6VUvtY6d8x2CXIhxtJa809P7uNgZSs7vnwpcWH+Y/Zp7OjjFztLeGjTnDHvv3a0ln/5yyFSowL54z2rSAgPYNCqqW/vJT7MX0LcTnVtvdz2249o7e7nL/evJfu8+dc91URBLn3kQoxDKcX3b1rIwKCV720rHHef775cyNN7Knlk++jpb/Mrmvn8nw+wKCmM5z63loRw26o8RoMiITxAQtwB4sL8eea+1QT5mbjrib2UztADXLOVBLkQE0iNCuILm7N49Wgd75x343NncT3bj9aSaQ5i+5Fa9p+yTbTVZxnkq38/SnxYAH+8Z9UFZzMU9kmODOTp+1Zj1XrSBTc8nQS5EBdw/8ZMsmKC+eZLBVQ02dah7Oqz8O1/FDI3NpgXHlxPXKg/33ulCKtV85t3T1La0Mn3b15IsJ+MJXC2THMwNyxJYE9ZE/0W6+Tf4KEkyIW4AF+TgR/dsojmrn6u+Ol7PLKtiO9vL6a6tYcf3ryIsAAfHr5mPker2/jvN47z6DulbF2awKZ5Ma4u3Wusz4qmu3+QQ6dbXV2Ky0iQCzGJFamRvPsfl/GxZUk8ubucZ/dVcufqFHKHlmW7cUkCS5PDeey9kwT7mfj29dkurti7rMmIwnDOVLveSIJciIsQG+rPjz6+mFe/eAlf3JzFw9fMH3nPYFB854ZsQvxMfPfGHKKC/VxYqfcJC/BhUWKYVwe5dOIJMQUL4kNZED92qNuylAgOfPtKux4eEtO3Piuax3eV0dln8cp7E/K3TggHkRB3nfVZ0Vismn3lTZPv7IHkb54Qwu2tSI3Az2Rgd6kEuRBCuCV/HyO5aRFe208uQS6E8AjrMqM5VtdBY0efq0uZcRLkQgiPsGFoJsQPT3pfq1yCXAjhERYmhhHqb5qR9VZnGwlyIYRHMBoUt+Um8/LhGp7Pr3J1OTNKglwI4TG+es181mVG8bUXjoxMZOYNJMiFEB7Dx2jg13cuJykikAeeyud0c7erS5oREuRCCI8SHujLE3fnYhm08o2XClxdzoyQIBdCeJwMczAfX5HM3rIm+iyDri7H6STIhRAeaVV6JH0WKwXVba4uxekkyIUQHmllWgQAe8s9/6anXUGulHpEKXVEKXVIKfWmUirBUYUJIYQ9ooL9yDQHsV+CfFL/o7VerLVeCmwDvu2AmoQQwiFWpUeSV9HCoFW7uhSnsivItdbt57wMAjz7T0sI4VZWpkXS0WvheF2Hq0txKrv7yJVSP1BKnQbu5AItcqXU/UqpPKVUXmNjo72nFUKISa0cWo7P0x8OmjTIlVI7lFIF43xtBdBaf0NrnQw8Azw00XG01o9rrXO11rlms9lxn0AIISaQFBFAQpg/+zy8n3zSNZG01ldc5LH+DGwHvmNXRUII4SBKKVamR/LhySa01iilXF2SU9g7amXOOS9vBI7ZV44QQjjWyrRIGjv6qGjy3Mf17V2l9L+UUvMAK1ABfM7+koQQwnFWpdv6yfedaiYtOsjF1TiHXUGutb7FUYUIIYQzZJmDCQ/0YX95M7flJru6HKeQJzuFEB7NYFCsSotkd+kZtPbMEdIS5EIIj3f5ghhq2noprGmffGc3JEEuhPB4m+fHohS8VVTv6lKcQoJcCOHxzCF+rEiJkCAXQgh3dmV2LEW17VS1eN4wRAlyIYRXuDI7FoAdHtgqlyAXQniFDHMwmeYg3iqWIBdCCLd1ZXYce8uaaesZcHUpDiVBLoTwGldmx2Kxat493uDqUhxKglwI4TWWJYcTHezHmx7WTy5BLoTwGgaD4vL5Mew63ohl0OrqchxGglwI4VU2zjXT0Wfh0OlWV5fiMBLkQgivsiErGoOCXSWes1KZBLkQwquEBfqwJDmc906ccXUpDiNBLoTwOhvnmDlS1UpLV7+rS3EICXIhhNfZONeM1rD7pGe0yiXIhRBeZ0lSGCH+Jo/pJ5cgF0J4HZPRwIasaHaVeMZiExLkQgivtHGumbr2Xk40dLq6FLtJkAshvNLGuWbAM4YhSpALIbxSYngAmeYg3pMgF0II97U+K5r8ihas1tH95NWtPbxeUOuiqqZOglwI4bUWJoTR3T9IRfPoVYN+/U4pn3v6AAcqW1xU2dRIkAshvFZ2QigAhTVto7Yfrba9/q9Xj7nFqBaHBLlS6t+VUlopFe2I4wkhxEyYExuMyaAoqmkf2dZvsXKstoPE8AD2nWpmZ/Hsn7vc7iBXSiUDVwKV9pcjhBAzx89kJCsmmMJzgrykvoP+QStf2TKP9OggfvT6sVk/5a0jWuQ/A74CzP7fP4QQ4jzZCaEU1Z4N8iNVtm6V5SkRfOXqeZxo6OTvB6pcVd5FsSvIlVI3AtVa68MXse/9Sqk8pVReY6P7D/cRQniGnIQwGjv6aOjoBeBodSvhgT4kRQSwZWEcy1LC+elbJfRbZm+rfNIgV0rtUEoVjPO1FfgG8O2LOZHW+nGtda7WOtdsNttbtxBCOER2vO2G53A/+ZGqNhYlhqGUQinFl66YS317H6/N4uGIkwa51voKrfXC87+AMiAdOKyUOgUkAQeUUnHOLVkIIRxneORKUW07vQODHK/rYFFi2Mj7l2RFkxYVyFMfVbiqxElNu2tFa31Uax2jtU7TWqcBVcByrXWdw6oTQggnCwuwdaMU1rRzrK4Di1WzOOlskBsMik+tSSWvomXU6JbZRMaRCyG8Xk5CKMU17SPjxxclhY96/9YVyfj7GHhqz/it8o7eAd4raXTZmHOHBflQy9wzZmkXQniV7Pgwypu62FPWRGSQLwlh/qPeDwv0YeuSRF46WE1bz8Co92rberj1sY+4+8l9vH3MNWPOpUUuhPB6OQmhaA1vFdaP3Og8311rU+kZGOTv+WeHIhbVtHPzox9S1dJDdLAvv91VNpNljzC55KxCCDGLDN/w7B+0juofP9fCxDCWpYTz2Hsnya9soavPQt6pFoL9TDz3ubXsLj3D97cXc+h0K0uTw8c9hrNIi1wI4fXiw/wJD/QBGDVi5Xxf2JyFj9FAcW07zV39bMiK5sXPr2NBfCi3r0ohxN/E47tOzlTZI6RFLoTwekopchJC2V3axKIJWuQAm+fHsvnh2HHfC/Yz8ak1qfz2vZNUNHWRGhXkrHLHkBa5EEIAl841k5MQSlyo/+Q7T+Az69IwGQw88UG5AyubnAS5EEIA92/MZPsXLxn3RufFign156ZlCfwt7zSt3f0OrO7CJMiFEMKB7liVQu+AlQ9KZ240tgS5EEI40KLEMIJ8jewta56xc0qQCyGEA5mMBlakRbK3vGnGzilBLoQQDrY6PZKS+k6au2amn1yCXAghHGxNRiQA+8pnpntFglwIIRxsUWI4/j6GGetekSAXQggH8zUZWJ4SMWM3PCXIhRDCCVanR1Fc105b98DkO9tJglwIIZxgdUYkWsP+U85vlUuQCyGEEyxNDsfXZGCfBLkQQrgnfx8jS5PD2Vvm/BueEuRCCOEkq9MjKahpp7PP4tTzSJALIYSTrM2MYtCqefe4c5eAkyAXQggnWZ0eRWJ4AM/uq3TqeSTIhRDCSYwGxSdXp7C7tImyxk6nnUeCXAghnOjW3CRMBuXUVrkEuRBCOFFMiD9X5cTyXH4VvQODTjmHBLkQQjjZnatTae0e4LWCWqccX4JcCCGcbG1GFOnRQTyzxzndK3YFuVLqu0qpaqXUoaGvax1VmBBCeAqDQfHJVSnkVbRwvK7D4cc3OeAYP9Na/9gBxxFCCI91y4ok3i89Q7/F6vBjOyLIhRBCTCIyyJc/3bPKKcd2RB/5Q0qpI0qpJ5VSERPtpJS6XymVp5TKa2xsdMBphRBCACit9YV3UGoHEDfOW98A9gBnAA08AsRrre+Z7KS5ubk6Ly9v6tUKIYQXU0rla61zz98+adeK1vqKizzB74Bt06hNCCGEHewdtRJ/zsubgQL7yhFCCDFV9t7s/G+l1FJsXSungAfsrkgIIcSU2BXkWuu7HFWIEEKI6ZEnO4UQws1JkAshhJubdPihU06qVCNQMc1vj8Y25NGbyGf2DvKZvYM9nzlVa20+f6NLgtweSqm88cZRejL5zN5BPrN3cMZnlq4VIYRwcxLkQgjh5twxyB93dQEuIJ/ZO8hn9g4O/8xu10cuhBBiNHdskQshhDiHBLkQQrg5twpypdQWpdRxpVSpUuphV9fjaEqpZKXUO0qpYqVUoVLqX4a2Ryql3lJKnRj674TzvrsrpZRRKXVQKbVt6HW6Umrv0Gf+q1LK19U1OpJSKlwp9bxS6tjQ9V7r6ddZKfWvQ3+vC5RSzyql/D3tOg+ty9CglCo4Z9u411XZ/HIoz44opZZP97xuE+RKKSPwKHANkA3coZTKdm1VDmcB/k1rvQBYA3x+6DM+DOzUWs8Bdg699jT/AhSf8/pH2JYRnAO0APe6pCrn+QXwutZ6PrAE22f32OuslEoEvgjkaq0XAkbgdjzvOv8B2HLetomu6zXAnKGv+4HfTPekbhPkwCqgVGtdprXuB/4CbHVxTQ6lta7VWh8Y+v8ObP+4E7F9zj8O7fZH4CbXVOgcSqkk4Drg90OvFbAZeH5oF4/6zEqpUGAj8ASA1rpfa92Kh19nbJP0BSilTEAgUIuHXWet9S6g+bzNE13XrcCftM0eIPy8qcEvmjsFeSJw+pzXVUPbPJJSKg1YBuwFYrXWtWALeyDGdZU5xc+BrwDDq9JGAa1aa8vQa0+71hlAI/B/Q91Jv1dKBeHB11lrXQ38GKjEFuBtQD6efZ2HTXRdHZZp7hTkapxtHjl2UikVDPwd+JLWut3V9TiTUup6oEFrnX/u5nF29aRrbQKWA7/RWi8DuvCgbpTxDPULbwXSgQQgCFvXwvk86TpPxmF/z90pyKuA5HNeJwE1LqrFaZRSPthC/Bmt9QtDm+uHf+Ua+m+Dq+pzgvXAjUqpU9i6yzZja6GHD/0KDp53rauAKq313qHXz2MLdk++zlcA5VrrRq31APACsA7Pvs7DJrquDss0dwry/cCcobvcvthulLzs4pocaqhv+AmgWGv903Peehm4e+j/7wb+MdO1OYvW+mta6yStdRq2a/q21vpO4B3g40O7edpnrgNOK6XmDW26HCjCg68zti6VNUqpwKG/58Of2WOv8zkmuq4vA/80NHplDdA23AUzZVprt/kCrgVKgJPAN1xdjxM+3wZsv1odAQ4NfV2Lrc94J3Bi6L+Rrq7VSZ//MmDb0P9nAPuAUuA5wM/V9Tn4sy4F8oau9UtAhKdfZ+A/gWPY1vZ9CvDztOsMPIvtHsAAthb3vRNdV2xdK48O5dlRbCN6pnVeeURfCCHcnDt1rQghhBiHBLkQQrg5CXIhhHBzEuRCCOHmJMiFEMLNSZALIYSbkyAXQgg39/8Bd2r3w9G8s/wAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(model_fit.fittedvalues)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercises\n",
    "\n",
    "1. Review the documentation on the Smoothing algorithms from https://www.statsmodels.org/dev/generated/statsmodels.tsa.holtwinters.ExponentialSmoothing.html See also the \"Next\" link to the left to view more algorithms.\n",
    "2. Check the autocorrelation for two currencies from Quandl (try the BUNDESBANK data source)\n",
    "3. Using a smoothing (whitening) algorithm, smooth the values of those currencies and check for autocorrelations in the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\marin\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency M will be used.\n",
      "  % freq, ValueWarning)\n",
      "C:\\Users\\marin\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\stattools.py:541: FutureWarning: fft=True will become the default in a future version of statsmodels. To suppress this warning, explicitly set fft=False.\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "C:\\Users\\marin\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency M will be used.\n",
      "  % freq, ValueWarning)\n",
      "C:\\Users\\marin\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\stattools.py:541: FutureWarning: fft=True will become the default in a future version of statsmodels. To suppress this warning, explicitly set fft=False.\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c8b80b8988>]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#ExponentialSmoothing?\n",
    "\n",
    "euro = quandl.get(\"BUNDESBANK/BBEX3_M_AUD_EUR_CM_AC_A01\")  # Euros in AUD\n",
    "\n",
    "euros = euro['Value']\n",
    "euros.name = \"EURO\"\n",
    "euros.head()\n",
    "\n",
    "usd = quandl.get(\"BUNDESBANK/BBEX3_M_AUD_USD_CM_AC_A01\")['Value']\n",
    "usd.name = \"USD\"\n",
    "usd.head()\n",
    "\n",
    "#ExponentialSmoothing?\n",
    "\n",
    "euro_model = SimpleExpSmoothing(euros)\n",
    "euro_fit = euro_model.fit()\n",
    "plt.plot(ts.acf(euro_fit.fittedvalues, nlags=100))\n",
    "\n",
    "usd_model = SimpleExpSmoothing(usd)\n",
    "usd_fit = usd_model.fit()\n",
    "plt.plot(ts.acf(usd_fit.fittedvalues, nlags=100))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/exponential_smoothing.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stationarity\n",
    "\n",
    "A stationary dataset is one where the main statistics are consistent throughout the given data, usually the mean and standard deviation. For instance, a time series with inflation would not be stationary, as it tends to grow overtime:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "import quandl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "platinum_prices = quandl.get(\"LPPM/PLAT\")['USD AM']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c8b800a148>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "platinum_prices.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we plot the moving average, we can see it tends to increase:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c8b80a8788>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "platinum_prices.rolling(365).mean().dropna().plot()  # Rolling n day window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see here that the mean is not consistent over time. This data is not stationary, which we can test more formally:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -1.67\n",
      "p-value: 0.45\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.tsa.stattools import adfuller\n",
    "result = adfuller(platinum_prices)\n",
    "print('ADF Statistic: {:.2f}'.format(result[0]))\n",
    "print('p-value: {:.2f}'.format(result[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the p-value is less than a given threshold (for instance 0.05) we would reject the hypothesis of a \"unit root\" and declare the dataset as stationary. Let's do the same test with our random values from before"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -10.18\n",
      "p-value: 0.00\n"
     ]
    }
   ],
   "source": [
    "result = adfuller(random_values)\n",
    "print('ADF Statistic: {:.2f}'.format(result[0]))\n",
    "print('p-value: {:.2f}'.format(result[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see here a p-value of (near) zero, which we would expect in this data as it has no time dependent structure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercises\n",
    "\n",
    "1. Compute the `adfuller` statistic for the currencies you extracted from Quandl earlier.\n",
    "2. A simple method of transforming data to be stationary is to compute the difference to the previous value. Difference your data to obtain a stationary dataset.\n",
    "3. Another method to create stationary data is transform the data using a log function. Compute the log of the currencies and recompute the adfuller statistic."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/adfuller.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CAPM - Capital Asset Pricing Model\n",
    "\n",
    "The CAPM model is a widely used model to determine expected returns for an asset and the impact of systematic risk. One method for calculating systematic risk is to measure the correlation between a stock and the market in general.\n",
    "\n",
    "The CAPM model is:\n",
    "\n",
    "\n",
    "$ \\bar{R_a} = R_f + \\beta (\\bar{R_m} - R_f)$\n",
    "\n",
    "Where:\n",
    "\n",
    "* $\\bar{R_a}$ is the expected return of the investment\n",
    "* $R_f$ is the risk free rate\n",
    "* $\\beta$ is the Beta of the investment (see below)\n",
    "* $\\bar{R_m}$ is the expected return of the market\n",
    "\n",
    "Note that the value $(\\bar{R_m} - R_f)$ is also known as the market risk premium.\n",
    "\n",
    "The Beta of an investment is the volatility of the stock, in relation to the market. If the stock moves with the market, it has a Beta around 1.0 (the market itself has, by definition, a Beta of 1.0). Stocks with low Beta values have less risk. High Beta values have high risk.\n",
    "\n",
    "To compute Beta, the equation is:\n",
    "\n",
    "$\\beta = \\frac{cov(a, m)}{var(m)}$\n",
    "\n",
    "Where $var(m)$ is the variance of the market, and $cov(a, m)$ is the covariance between the market and the given asset.\n",
    "\n",
    "#### Extended Exercise\n",
    "\n",
    "1. Download the S&P 500 data from Quandl. Use the dataset search to find an appropriate data source.\n",
    "2. Compute the percentage change on a daily basis as a value between 0 and 100% - not a decimal. You'll need the closing price.\n",
    "3. Repeat steps 1 and 2 for a given stock (the provided solution uses Coca Cola)\n",
    "4. Compute the Beta value, using the prices for the period 2016 to 2018 inclusive\n",
    "5. Compute the CAPM value, with a risk free rate of 2.5% (or another if you have a preferred risk free investment). Hint: CAGR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Market Variance: 0.7265414157716941\n",
      "Stock Covariance: 0.4684920443273424\n",
      "Beta: 0.6448249668323929\n",
      "Return on Market: 0.0772352134654195\n",
      "CAPM: 0.058682569790322096\n"
     ]
    }
   ],
   "source": [
    "sp500 = quandl.get(\"CHRIS/CME_SP1\")\n",
    "\n",
    "sp500_sample = sp500.loc[\"2016\":\"2018\"].dropna()\n",
    "\n",
    "market = sp500_sample['Last'].pct_change().dropna() * 100\n",
    "\n",
    "cola = quandl.get(\"WIKI/KO\")\n",
    "\n",
    "cola_sample = cola['2016':\"2018\"]\n",
    "\n",
    "coca = cola_sample['Close'].pct_change().dropna() * 100\n",
    "\n",
    "market_variance = market[\"2016\":\"2018\"].var()\n",
    "print(f\"Market Variance: {market_variance}\")\n",
    "\n",
    "stock_cov = market.corr(coca)\n",
    "\n",
    "print(f\"Stock Covariance: {stock_cov}\")\n",
    "\n",
    "beta = stock_cov / market_variance\n",
    "\n",
    "print(f\"Beta: {beta}\")\n",
    "\n",
    "e = ending_balance = sp500_sample.iloc[-1][\"Last\"]\n",
    "s = starting_balance = sp500_sample.iloc[0][\"Last\"]\n",
    "n = number_years = 3  # 2016, 2017, 2018\n",
    "return_on_market = (e / s) ** (1 / n) - 1\n",
    "\n",
    "print(f\"Return on Market: {return_on_market}\")\n",
    "\n",
    "capm = .025  + beta * (return_on_market - .025)\n",
    "print(f\"CAPM: {capm}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/capm.py`*"
   ]
  }
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